The ministry said that preliminary tests showed a batch of the medicine contained ethylene glycol, a toxic substance.
The children were given the Dok-1 Max syrup without a doctor's prescription, it said. The amount they consumed also exceeded the standard dose for children.
The allegation from Uzbekistan comes weeks after The Gambia also linked child deaths to cough syrups made by another Indian firm.
India's health ministry said in a statement that its officials have been in regular contact with the national drug regulator of Uzbekistan regarding the matter since December 27, 2022.
It added that health officials have conducted an inspection of Marion Biotech's facility in Noida in Uttar Pradesh state.
"The samples of the cough syrup have been taken from the manufacturing premises and sent to Regional Drugs Testing Laboratory, Chandigarh for testing," the statement added.
News agency ANI has quoted a Marion Biotech executive as saying that the company has halted production of the syrup temporarily. He added that the government was conducting an enquiry and that the firm would take action accordingly.
Marion Biotech is based in Noida, near India's national capital Delhi. Its website is currently down, but the company's LinkedIn page says it was founded in 1999 and that its products are household names in Central Asian countries, Central and Latin America, South East Asia and Africa".
India produces a third of the world's medicines, mostly in the form of generic drugs.
The country, home to some of the fastest-growing pharmaceutical companies, is known as the world's pharmacy and meets much of the medical needs of developing countries.
The Uzbek ministry statement, dated December 27, says that Dok-1 Max tablets and syrup have been sold in the country since 2012.
"It was found that the deceased children, before admission to hospital treatment, took this drug at home for 2-7 days, 3-4 times a day, 2.5-5ml, which exceeds the standard dose of the drug for children," the ministry said.
The statement did not specify over what time period the deaths occurred. BBC Monitoring had reported on December 23, citing news website Gazeta.uz, that Uzbek authorities were investigating claims that 15 children died in central Samarkand region over the past two months after taking a cough syrup made in India".
On December 26, Podrobno.uz news website reported that 21 children - 15 of them under the age of three - were treated for acute kidney failure allegedly caused by the India-made cough syrup Dok-1 Max between September and December". Three of the patients recovered.
The ministry also said that preliminary laboratory studies have shown that this series of Dok-1 Max syrup contains ethylene glycol.
In October 2022, the World Health Organization (WHO) had sounded a global alert and linked four India-made cough syrups to the deaths of 66 children from kidney injuries in The Gambia. It said tests on samples of the syrup showed that they contained unacceptable amounts of toxic substances diethylene glycol and ethylene glycol.
Both the Indian government and the company, Maiden Pharmaceuticals, have denied the allegations.
India said earlier in December that tests on the four syrups showed that they complied with specifications, and a government official told the BBC that the WHO had been presumptuous in blaming the syrups. But the WHO said it stood by the action taken.
Last week, a parliamentary committee in The Gambia recommended the prosecution of Maiden Pharmaceuticals after weeks of investigation. The committee also recommended banning all products by the firm in the country.
