In 2289, he and T'Meni sent their son Tuvok to Starfleet Academy, as it was their wish that he become a Starfleet officer. Feeling obliged to honor his parent's wishes, Tuvok consented to attend. (VOY: "Flashback")
According to the officially licensed Star Trek: The Magazine, the names of Tuvok's parents are T'Meni and Sunak. Of these names however, his mother was the only one who was ever canonically referred. Although never named on screen, Tuvok's father was mentioned as having sent a letter from aboard the USS Yorktown in "Flashback"; as such, it can be presumed that he was a member of Starfleet.