Any clue about William Shakespeare’s life usually excites scholars, but one piece of evidence had been neglected for decades. Now, a new analysis of that overlooked document seems to shatter a longstanding narrative about the Bard’s bad marriage.

Shakespeare was 18 in 1582 when he married Anne Hathaway, the daughter of a family friend in Stratford-upon-Avon who was in her mid-20s and pregnant. For centuries, it was thought that the writer left his wife and children behind to lead a literary life in London, seeking to avoid “the humiliation of domestic feuds,” as one influential 19th-century essayist put it.

This view of Shakespeare’s wife as a “distant encumbrance” suited scholars who thought “Shakespeare was far too interesting to be a married guy,” Matthew Steggle, a literature professor at the University of Bristol in England, said in an interview. The perception was bolstered by the fact that Shakespeare had famously bequeathed her his “second best bed” in his will.

But Mr. Steggle’s new research, expected to be published this week in the journal Shakespeare, suggests that the writer was not detached from his marriage after all.

The hint lies in a fragment of a 17th-century letter addressing a “Mrs Shakspaire,” found in the binding of a book published in 1608. The letter’s existence was noted in 1978 by an amateur historian, but it got minimal attention, even after the book was unbound in 2016, revealing what appeared to be part of a reply from Shakespeare’s wife, Mr. Steggle said.

He was working on a Shakespeare biography when he learned of the 1978 find, and was surprised it wasn’t better known. Technological advances allowed him to track down people mentioned in the long-ago correspondence, along with other evidence indicating that it included the playwright’s wife, he said.