The Togo international striker has struggled for form at White Hart Lane this season, scoring just twice in 12 appearances across all competitions.
Spurs have not revealed the reasons for Adebayor's absence and no timescale has been put on a return.
"We can confirm that Emmanuel Adebayor has been given permission to return home for personal reasons," Spurs, who face Besiktas in the UEFA Europa League on Thursday, posted on Twitter.
"This is a private matter and so we will not be providing any further comment."
Adebayor has slipped out of Mauricio Pochettino's first-team plans recently, with Harry Kane and Roberto Soldado preferred.
The 30-year-old's last appearance came as a second-half substitute in the 2-1 defeat at home to Stoke City on November 9.
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