The drugs, known as proton pump inhibitors (PPIs), are often prescribed to treat issues such as acid reflux, heartburn and stomach ulcers. They work by blocking the enzyme in the wall of the stomach that produces acid.
Researchers have advised patients who take the drugs to only use them when medically necessary, after a study found they could increase risk of kidney failure by up to 96%.
There are five PPIs licensed for use in the UK. These are:
Researchers analysed the data of 170,000 people taking PPIs and 20,000 people taking an alternative class of drugs used to suppress stomach acid, called histamine H2 receptor blockers.
They found that, over a period of five years, those who took PPIs had a 28% increased risk of developing chronic kidney disease.
They also had a 96% greater risk of suffering kidney failure.
"The results emphasise the importance of limiting PPI use to only when it is medically necessary, and also limiting the duration of use to the shortest possible," said study author Dr Ziyad Al-Aly, from the VA Saint Louis Health Care System in the US.
"A lot of patients start taking PPIs for a medical condition, and they continue much longer than necessary."
The study, which was published in the Journal of the American Society of Nephrology, isn't the first to link heartburn drugs to health problems.
A study published in February 2016 suggested that heartburn drugs could increase a person's risk of developing dementia.
Researchers found that those who used proton pump inhibitor drugs (PPIs) at least once every three months were 44% more likely to develop dementia in later life than those who did not take the drugs.
Dr Helen Webberley, the dedicated GP for Oxford Online Pharmacy, said PPIs are "excellent at reducing acid", but it can be difficult to come off them once you've started taking them regularly.
"PPIs are a good example of a drug that causes reliance," she said. "When you stop them you get a rebound worsening in acid reflux and indigestion, which makes you want to take them more.
"My advice is to always discuss plans to stop medication with the prescriber, be that your doctor or pharmacist.
"If you would like to withdraw from PPIs reduce your intake slowly, first by taking them on alternate days and then every three days until your body gets used to the medicine being withdrawn from your system."