Yes — amoxicillin (an antibiotic) and ibuprofen (a painkiller) work in completely different ways and are commonly taken together, but stick to the dosing on the labels and check with your pharmacist if you have stomach, kidney, heart, or bleeding problems.
Amoxicillin is a penicillin-type antibiotic that fights infection by stopping the growth of bacteria, while ibuprofen is an NSAID that relieves pain, fever, and inflammation — different drugs doing different jobs, so there's no expected interaction between them. The NHS list of medicines that interact with amoxicillin (warfarin, methotrexate, probenecid, allopurinol, and other antibiotics) and the MedlinePlus amoxicillin page do not flag ibuprofen or other NSAIDs at all. In fact, an NSAID like ibuprofen is a normal choice for the pain or fever that often accompanies the infection an antibiotic is treating.
The cautions here come from ibuprofen itself, not the combination: take the lowest effective dose for the shortest time and don't exceed the maximum on the label, and don't combine it with other NSAIDs or aspirin (that raises the risk of stomach ulcers and bleeding). Ibuprofen may be unsuitable if you have or have had a stomach ulcer, a heart/liver/kidney condition, blood-clotting problems, or a prior stroke, and it can interact with warfarin, steroids, antidepressants, and blood-pressure medicines — so ask a pharmacist or doctor first if any of these apply to you. Watch for warning signs like black or bloody stools, vomiting blood, severe stomach pain, or much less urine than usual, and stop and seek medical help if they occur. Also finish the full amoxicillin course even once you feel better, and call your clinician if your infection isn't improving or you develop signs of an allergic reaction (rash, swelling, trouble breathing).
This is general reference, not medical advice, and not a guarantee of safety. Interactions depend on your doses, health conditions, and other medicines. Always confirm with your pharmacist or doctor before combining products, and follow the dosing on each label.