Kane, who is out with a torn hamstring until April, tweeted twice during the first half of the Premier League game at Tottenham Stadium on Saturday.
The first included a photo he seemed to have taken himself. It showed his leg in a brace resting on a duvet and, beyond his foot, a television showing Japhet Tanganga, a young defender who making his first Premier League start for Spurs.
"Surgery went very well. First day of recovery starts now!" said the text adding "#COYS," for Come On You Spurs.
The second photo, taken from the opposite end of the hospital bed, showed Kane in a robe smiling and giving a thumbs up with just the hashtag "COYS".
Spurs lost 1-0.
The 26-year-old has scored 27 goals in 31 appearances for club and country this season.
He suffered the injury while taking a shot during Tottenham's Premier League defeat at Southampton on New Year's Day and limped away from St Mary's on crutches.