Kane suffered ankle ligament damage in the 6-0 FA Cup win over Millwall and is not expected to return before the end of April.
Spurs win over Everton on March 5 secured a club-record nine consecutive wins at White Hart Lane, where they have not tasted defeat since Southampton came to town in May last year.
Southampton have not been in action since a dramatic 4-3 away win at Watford on the same weekend, the second game on the trot they netted four times, and will no doubt be keen to all but extinguish their former manager's title bid.
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Tottenham host Southampton with kick-off scheduled for 2.15pm on Sunday, March 19.
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Harry Kane is the latest key first-team member to be sidelined, with Danny Rose already out, with a second ankle ligament injury of the season.
Heung-min Son - who scored a hat-trick against Millwall - will likely deputise, but Vincent Janssen's first goal this season from open play in the same game has boosted his chances.
Elsewhere, Mauricio Pochettino will likely stick with the same 10 who have featured in recent weeks.
Southampton have had two weeks to prepare and recuperate players, but the game will come too soon for Charlie Austin and Matt Targett.
Tottenham starting XI: Lloris; Dier, Alderweireld, Vertonghen; Walker, Wanyama, Dembele, Davies; Eriksen, Dele; Son
Southampton starting XI: Forster; Cedric, Stephens, Yoshida, Bertrand; Ward-Prowse, Romeu, Davis, Redmond; Tadic; Gabbiadini
BETTING ODDS (via 888 Sport)
- Tottenham to win: 8/11
- Southampton to win: 4/1
- Draw: 14/5
Click here to place a bet. Odds correct as of March 19 at 9:45am