The 30-year-old former Arsenal and Manchester City player has been given permission to take time off, Spurs said on their website.
"This is a private matter and so we will not be providing any further comment," the club added.
Adebayor has made 12 appearances for Tottenham this season and has not played since the November international break when Togo failed to qualify for the 2015 Africa Cup of Nations.
Spurs visit Turkish side Besiktas in the Europa League on Thursday, needing at least a point to top their group having already sealed a place in the round of 32.
(Reporting by Martyn Herman; editing by Ken Ferris)
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