Kane was substituted after failing to score in England’s first two Group D matches against Croatia and Scotland.
The Tottenham striker has yet to register a shot on target and there were calls for him to be dropped following his subdued display in Friday’s drab 0-0 draw with Scotland.
But England boss Southgate on Sunday revealed he would keep faith with the 2018 World Cup Golden Boot winner.
“You can assume that, yes, absolutely,” Southgate said when asked if Kane would keep his place.
“He is fundamental not only to the goals he scores but the build-up play and everything else he brings.
“I know there will be a lot of questions being asked about him at the moment but he has been through that 100 times before.
“I have answered that in this role several times in the past and he has come up with the goals that have won us the next games and I expect that to be the same moving forward.”
England remain on course for the last 16 with four points and will win the group if they beat the Czechs.
But their uninspired attacking displays have limited them to one goal and only three shots on target in their two matches.
If they are to win the tournament, they need Kane to recapture the form that saw him finish as the Premier League’s top scorer with 23 goals this season.
– ‘Most important player’ –
Kane often drops deeper to get involved in the play with Tottenham and has created a host of chances for club colleagues.
Taking a similar approach at the European Championship has seen Kane’s goal-scoring opportunities dry up.
But Southgate said his decision to replace Kane in both games was down to a desire to keep him fresh after he lost momentum during England’s run to the World Cup semi-finals three years ago.
“In one of the games we were already ahead and we needed energy to press and keep the lead, we didn’t need an additional goal,” he told ITV Sport.
“Harry, during the World Cup, we ended up with him playing a lot of football and we’ve felt the need to manage that load a little bit this time and we have got good options on the bench to bring people into the game.
“But he is our most important player, there is no doubt about that, you’ve only got to look at his goalscoring record with us to see his importance to the team.”
Atletico Madrid right-back Trippier played with Kane for several years at Tottenham and is sure he will get back on track soon.
“I believe in Harry and I know he will score goals, Harry’s chances will come and for sure he will score goals,” Trippier said.
“Harry has had an unbelievable season with Spurs. He is working hard in training and it is about getting the chances to him.
“With Harry, he works so hard for the team and people might not recognise what he does off the ball.
“He is our captain, our leader, a big player for us and we just need to create chances for him to score goals. We need to get him on the end of chances.”
