The 28-year-old has only made 15 appearances this season due to fitness problems, and he is again on the sidelines with a muscular problem which was aggravated last month.
Shaw started against both Aston Villa and Luton Town on February 11 and February 18 respectively, but he was replaced at the interval in the two fixtures and has not been seen since the clash with Luton.
There have been suggestions that the England international's injury will keep him out for the rest of the season and also prevent him from featuring for his country at Euro 2024.
However, speaking during his press conference to preview Saturday's Premier League game against Brentford, Ten Hag said that he is expecting to have the left-back fit and available before the campaign finishes.
Shaw on course to feature before the end of the season
"Yes, I expect him back, I think before the end of the season," Ten Hag told reporters on Friday. "That is the plan, and he is still on schedule for this. He will return into our team."
Man United have another 10 Premier League matches this season, with the team currently battling to secure a spot in the 2024-25 Champions League.
The 20-time English champions are fifth in the table, six points behind fifth-placed Tottenham Hotspur and nine from Aston Villa, who have played a game more than the two sides directly below them.
Ten Hag's side are also chasing silverware in the FA Cup this season, with Coventry City their opponents in the semi-final of the competition on April 21 ahead of a potential final against Manchester City or Chelsea.
Man United could move for a new left-back this summer
The Red Devils will allegedly be in the market for a young left-back this summer, with the team struggling in that area of the field during the 2023-24 campaign.
Tyrell Malacia has not played a single minute of football this season due to a knee injury which has required two separate operations.
The Netherlands international featured 39 times for Man United last season following his arrival from Feyenoord, but there are thought to be concerns over his long-term fitness.
Alvaro Fernandez and Brandon Williams, meanwhile, are out on loan at Benfica and Ipswich Town respectively, and neither are believed to be in the club's plans moving forward.
As a result, Man United are said to be keen to boost the position this summer, with Victor Lindelof and Aaron Wan-Bissaka recently featuring on the left side of the defence, and Girona's Miguel Gutierrez is thought to be admired by the English giants.