Since medicine was not nearly what it is today, nor are there any surviving medical records, no one can be 100% sure. But most educated guesses are that Washington was infertile. His wife, Martha, had four children by her first marriage before becoming a widow, and there isn't any evidence that anything happened during her last pregnancy to conclude that she was incapable of having further children.

Exactly what would have caused Washington's infertility is even more speculative than the infertility itself.

What is known is that, from surviving letters, George and Martha Washington did have a loving relationship, which was presumably of a sexual nature because Washington lamented in at least one surviving letter that he wished he and Martha had produced an heir.

Here is one scholarly analysis of the subject, though again, this is educated speculation about his fertility since there are no medical records to consult.