Patients taking a class of painkilling drugs called Cox-2 inhibitors have been advised to contact their GP to review their treatment.
Celebrex is used to treat arthritis
The advice follows a study suggesting one of the drugs, Celebrex, increased the risk of heart problems.
The Medicines and Healthcare products Regulatory Agency advice applies to people taking Celebrex, Bextra and Arcoxia.
The agency stressed their was no need to make an urgent appointment.
Patients who have established heart disease or who are at high risk of stroke will have their treatment changed.
For all other patients, alternative treatments will be considered on the basis of their medical history.
Celebrex, manufactured by Pfizer, and other drugs of the same type are used in the treatment of pain and inflammation in osteoarthritis and rheumatoid arthritis, and in the management of acute pain.
Celebrex is used by an estimated 600,000 patients in the UK.
The new advice follows a study by the US Cancer Institute which found patients were at an increased risk of heart attack and stroke after taking Celebrex.
The study, of 2,400 patients, found that patients who took a dose of 400mg of Celebrex a day were 2.5 times more likely to have a heart attack or stroke than people taking a placebo.
Those taking a 800mg daily dose were at 3.4 times the risk.
An alternative Cox-2 inhibitor, Vioxx, was withdrawn by its makers Merck in September following similar concerns.
In that long-term study taking Vioxx for 18 months or more was linked to an increased risk of heart attack and stroke.
Professor Gordon Duff, chairman of the Committee on the Safety of Medicines, said: "Patients taking any of these drugs should contact their doctor at the next
convenient appointment to discuss their treatment.
"The Committee on the Safety of Medicines is waiting for the study data. Once this is available, the committee will carefully consider this and issue further advice."
Cox-2 inhibitors are marketed as a safer alternative to the more traditional non-steroidal anti-inflammatory drugs (NSAIDs) which are associated with side effects.
The European Medicines Evaluation Agency is currently assessing their use.
Pfizer issued a statement in which it said it was working carefully to evaluate the information and liaising with the regulatory authorities to fully understand it's implications for patients.
Chief executive officer Hank McKinnell said on Monday that the company had no plans to withdraw Celebrex.
Instead, he predicted that the US regulatory authority, the Food and Drug Administration, would adjust the labelling of the product.
Mr McKinnell said: "We fully expect that Celebrex will be found safe and effective when taken as directed."
Dr Jim Kennedy, of the Royal College of GPs, said: "We do not know the full results of this (Celebrex) study and do not want to see patients unduly worried.
"If patients are concerned, we would advise them to stop taking these medicines and use another pain-killer, which their local pharmacist will be able to advise them on.
"In addition, we also advise patients, particularly those with established heart disease or who are at high risk of stroke, to follow the MHRA advice and make a routine appointment with their GP to discuss a possible alternative prescription.
"Patients should be reassured that there are several other treatments available for arthritic pain relief. We look forward to seeing the results of this study as soon as possible."