Studies in healthy people found that esomeprazole has no significant interaction with medicines processed by the liver's cytochrome P450 system. The medicines tested include ibuprofen, warfarin, phenytoin, propranolol, diazepam, clarithromycin and a few others. So taking this combination with ibuprofen is not expected to cause a problem.
These medicines are often taken together with some care. Your doctor may change a dose, space them apart or check on you more often. Make sure your doctor and pharmacist know you take both.