Southgate has rotated the captain’s armband since easing former skipper Wayne Rooney out of his squad and with Rooney having since retired from international football, England do not have a permanent captain.
Henderson, 27, captained the team in England’s 4-0 win away to Malta on Friday and Southgate said he would lead the team out against Slovakia at Wembley.
Southgate told reporters at Tottenham Hotspur’s training ground in Enfield, north London there was “no point” changing the captaincy.
Tottenham left-back Danny Rose and Liverpool midfielder Adam Lallana are not in the squad due to injury, but Southgate reported no new injury problems after Sunday’s final pre-game training session.
England are two points clear of Slovakia at the top of UEFA qualifying Group F and if they win on Monday, they will require only two points from their last two games to secure their place in Russia.
“It’s a great opportunity for us, a home game,” said Southgate.
“We are playing good opposition so we’ve got to make sure we are tactically prepared, which we will be, but also we’ve got to have belief in the team that we’ve got.
“We’ve got some exciting players and we want to show that. We know the task we have. We know the opportunity. The whole country wants to be at a World Cup.”