Zamzam water is mineral:

Between 1973 and 1980, Zamzam water was chemically analyzed by well-known international specialized companies, and the results were amazing. They indicated that Zamzam water had no trace of any polluting bacteria. Moreover, it is considered as a mineral water. 

Mineral water is defined as a kind of water which contains 150-350 milligrams of mineral salts per liter. 

This kind of water is bottled and sold to people. Zamzam water contains 2000 milligrams of mineral salts per liter, some of which are Calcium, Sodium, Magnesium, Potassium and others.

The Blessed water

Interviewer:
Does this water have any qualities that make it special in regards of worship, or any other qualities?
Dr. Nabulsi:
There are a lot of facts about this water and I will mention them inshaallah.

Zamzam water is the richest water in Calcium,

for it reaches 200 milligrams in one liter. The words of the prophet (PBUH) were very true when he said:

((Verily, it is blessed, it is a food that nourishes))

((... and a healing for sickness.))

As you know, the skeleton of the human being has the ability to renew its cells and it has what is called "destruction and instruction process". If one neglects his body’s need of calcium, his skeleton will be at risk of having osteoporosis 

or osteomalacia (bone loss) which is a serious disease, and in such cases any fraction in the pelvic at an old age will be a disaster.

((It is a food that nourishes))

Facts and numbers:

Scientific research showed that people who drink this water has lower chance to be infected with arteries diseases

The prophet (PBUH) said:

((... and a healing for sickness.))  

Each word said by the prophet (PBUH) means a scientific truth that scientists have discovered recently. Water is considered as carbonated and digestive if it contains more than 250 grams of bi-carbonates per liter. The most famous mineral water in the world is that of the spring of Ivian (France), in which the rate of bi-Carbonates is 357 mgs/liter.

As for Zamzam water, the rate of bi-Carbonates is 366 mgs/liter.

Yes, indeed! Allah’s Messenger, (PBUH), speaks the truth as he says, 

((Zamzam water is (proper) for whatever (purpose) it is drunk for.))

Interviewer:
Dear sir, did scientists, especially doctors, consider prescribing this water to their patients in order to cure specific diseases?
Absolutely, for the prophet (PBUH) said:

((... and a healing for sickness.))

Hence, let us look for the specific medical indications of this water.
 By the way, I consider the following Hadith as a prophetic miracle, Jaber narrated that the prophet (PBUH) said:

((Every illness has a cure, and when the proper remedy is applied to the disease it cures it with the permission of Allah))

[Sahih Muslim]

 If this Hadith were to be read by a patient, his heart would be filled with hope and trust in Allah the Almighty, on the other hand, if it were to be read by a doctor, he would feel that he can do a lot more.

((Every illness has a cure...))

 There is still one illness which I call the exit illness, and which has no cure, it is the illness of death. It all starts with an intractable disease in a part of the body that gets worse by time and leads to death even if the afflicted was a prophet, a notable person or a pious one, for the illness of death is the human exit from this life (to the other world) and it is the incurable disease unlike other diseases included in the following hadith:

((Every illness has a cure...))

Back to answer your question: In a book that was published in 1995, medical scientists mentioned that the mineral water is good for a lot of rheumatic diseases,

for peptic acidity, for chronic diarrhea, and for indigestion.  Moreover it has diuretic effect, laxative effect and it restores the lacked minerals in the body.

The prophet's words were true when he said:

((If you drink it seeking health, Allah will give you healing, if you drink it seeking refuge with Allah, Allah will grant you refuge and if you drink it to quench your thirst, Allah will quench your thirst.))

Drinking Zamzam water as a worship

The question to be asked is: Why drinking Zamzam water is considered as an act or worship? To answer this question: Zamzam water is kind of salty water,

whereas man long for sweet water. Thus since Muslims drink this water despite its salty taste because they believe that it is a blessed water, not to mention drinking of this water till one is full, this action is a proof of their faith.
To apply the previous prophetic instructions, the noble companions, their followers and lot of scholars and common people were keen to reach Tadullo' (drinking till one is full) of Zamzam water especially when they were performing Hajj (the obligatory pilgrimage to Mecca) and Umrah (the supererogatory pilgrimage performed in Mecca).  The word Tadullo' is taken from Del' (rib) and Tadullo' means to fill the ribs from this water accompanied by a specific intentionwhen drinking it, for supplication is commendable when you drink Zamzam water

and that is because Zamzam is for whatever it is drunk for. It was narrated that Umar Ibn Al Khattab, May Allah be pleased with him, used to say the following supplication when he drank Zamzam water:

 ((O Allah, I am drinking it to ward off my thirst on the Day of Resurrection.))

 It was also narrated that Ibn Abbas used to say when drinking Zamzam water:
 

((O Allah, I ask you to grant me beneficial knowledge, plentiful provision and healing from every disease))