Boston Mayor Thomas M. Menino voted Tuesday by absentee ballot because he remained hospitalized with a viral infection and a back injury.

Menino completed his ballot on Friday at Brigham and Women’s Hospital, where he has spent 12 days recuperating. Doctors have not indicated when he will return home or how long Menino will need to convalesce before returning to City Hall, but his condition continues to improve, said his spokeswoman, Dot Joyce.