Generally yes for most healthy people — probiotics are commonly taken alongside antibiotics and the combination isn't expected to cause a dangerous interaction, but check with your pharmacist or doctor first, especially if you're seriously ill or have a weakened immune system.
Probiotics are live bacteria or yeasts, not drugs that act on the same pathways as antibiotics, so there's no recognized dangerous chemical interaction between the two. In fact, the NCCIH notes that giving probiotics along with antibiotics was associated with about a 50% lower likelihood of antibiotic-associated diarrhea, and that it is "moderately certain" that probiotics can reduce the risk of C. difficile diarrhea in adults and children receiving antibiotics. That said, the research doesn't yet establish which specific probiotic strains or doses are helpful, and benefits should not be overstated. The NHS says probiotics appear safe for most people with a healthy immune system.
This combination is not appropriate for everyone: the NHS advises that anyone with an existing health condition or a weakened immune system talk to a doctor before taking any probiotic, and the NCCIH warns that the risk of harmful effects from probiotics is greater in people with severe illnesses or compromised immune systems. Critically, the FDA has warned health care providers that severe or fatal infections have been reported in premature infants given probiotics — do not give probiotics to a premature baby without a doctor's direction. For everyone else, follow the dosing on the product label, and because some antibiotics interact with other medicines and supplements, run your specific antibiotic and any supplements past your GP or pharmacist first. Stop and seek medical advice if you develop signs of infection (fever, worsening illness) or severe or bloody diarrhea, which can signal a serious gut infection rather than a probiotic benefit.
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.