The hosts took a shock lead when Robin Quasion managed to turn inside the United half before firing an unstoppable curling shot past substitute keeper Ben Amos just after the break.
United responded with 20 minutes remaining when substitute Henriquez turned in Wilfried Zaha’s cutback - but the Premier League champions failed to find a winner.
The visitors created a host of chances throughout the match with Robin van Persie twice missing from six yards and Nemanja Vidic heading against the bar from a corner, but they will be concerned by injuries to Nani and Jonny Evans.
The pre-match talk centred on the future of Wayne Rooney after the striker pulled out of the friendly with an injury. When it began, it was at a frantic tempo with both sides keen to exploit the flanks with Nani in particular looking lively.
And it was the Portuguese winger who fashioned the first opening when he found Zaha inside the area, but the former Palace player sliced his shot wide.
Van Persie was next to go close, cutting in from the right flank after being found by Rafael and whipping a low shot narrowly past the post.
The Dutchman was then slipped in by Nani but his left-footed effort was saved superbly by an outstretched Kenny Stamatopoulos glove.
Both sides then had the chance to take the lead in a frantic minute as the game began to really open up.
First Martin Kayongo-Mutumba controlled a long ball over the top and fired in a shot which forced Anders Lindegaard into a good stop before United raced down the other end, with Van Persie somehow failing to turn Patrice Evra’s cross into the net.
Kennedy Igboananike then blasted straight at Lindegaard and Mutumba flashed wide as the hosts finished the half strongly.
AIK carried their momentum into the second half and took an unlikely lead when Quasion turned inside the United half before unleashing a stunning shot into Amos’s top corner.
The goal appeared to snap United into action and they almost responded immediately when Vidic rose well to meet a corner but his header bounced into the turf, up and onto the crossbar.
A flurry of substitutions threatened the match’s flow but United managed to level when Zaha’s driven pass across the face of goal set up Henriquez for a simple finish.
The Chile striker, who joined from Universidad de Chile a year ago, was loaned out to Wigan last season, where he suffered relegation but won the FA Cup.
He seems set to get his chance at Old Trafford this season under David Moyes. And he could have scored a second, but failed to get the ball out of his feet and shoot for goal after advancing into the box.
Despite plenty of late pressure United failed to find a winner as substitute Danny Welbeck failed to prod past Patrik Carlgren in the AIK goal before Van Persie missed a simple header from six yards out.