Danish scientists found those taking the combined pill, the most common form of contraception used in the UK, are most likely to experience the life-threatening emergency.
They said that although the risk of a blood clot was low, women should be aware of the risks.
Blood clots are dangerous since they can lodge in the lungs causing breathing and heart problems.
The study, which involved more than two million women, found those on newer combined pills like Yasmin or Lucette were at greatest risk.
Women taking the mini pill or using implants and coils were much less likely to experience the event.
Previous studies have shown that the painkiller can increase the risk of stroke.
But this is the first time a link has been found between the drug and hormonal contraception.
Researchers from the University of Copenhagen, investigated the medical records of healthy women between the ages of 15 to 49 years over 21 years.
The study, published in the British Medical Journal, found women who take anti-inflammatories while on the Pill were 1.5 times more likely to have a blood clot, compared with those who were not using hormonal contraception.
Out of every 100,000 women who took NSAIDs while on the pill, 23 suffered a stroke each week, while only four clots happened per week among women not taking the contraceptive.
It also found diclofenac was the anti-inflammatory drug most likely to trigger an event, compared with ibuprofen and naproxen.
Study author Dr Amani Meaidi, said: “Women needing both hormonal contraception and regular use of anti-inflammatories should be advised accordingly.”
Dr Ian Musgrave, from the University of Adelaide, said the study gives rise to “unwarranted concern” as the risk of clotting is low.
He added: “Nonetheless this study provides good evidence that women on hormonal contraception who are at high risk of clotting events have an increased risk when on NSAIDs (anti-inflammatories).”