Kane returned to action for Tottenham after a two-month lay-off in the recent north London derby and joined up with the England squad to face Scotland and Spain.
The striker didn't play any part in the 3-0 victory over Scotland and has been released back to Tottenham to continue his recovery from injury.
"Harry reported for us last week having not played a full game for some seven weeks but Tottenham were more than happy for him to come with us," Southgate said.
"It was never really my intention to start him in a game and I think it's important that he gets a different training programme to what we're going to follow over the next couple of days.
"I'm really grateful to Tottenham for letting us have him for the qualifier. Once we'd assessed our injury status and the fact we were fine and covered for what we'd do for this game, the sessions that we're going to do aren't what Harry needs at this time, having had such a long lay-off".