The run began with a second division game against Fulham at Craven Cottage in 1937, Reuters reported.
The current crop includes Marcus Rashford and Scott McTominay, who are following in the footsteps of greats such as Bobby Charlton, George Best and the “Class of 92”.
"Giving young players a chance is a tradition that we are very proud of. It's part of our DNA and you learn that quickly when you join the club," Solskjaer said in a statement.
“Nothing gives me more pleasure than seeing a player that has come through our academy thriving on the pitch.
“Young players can only surprise you and impress you when you give them a chance to show their talent. It’s a milestone that we are proud of and long may it continue.”
United has already handed 10 first team debuts to academy graduates this season and youth players have accounted for more than a third of the total minutes played by all first team members.
“The ultimate aim for the academy is to get players into the first team and for that to have happened for 4,000 consecutive games is an extraordinary achievement,” Nicky Butt, the head of United’s first team development, added.
Butt was another member of the Class of 92 that included the likes of Gary Neville, David Beckham and Paul Scholes, who were part of United’s glory years under manager Sir Alex Ferguson throughout the 1990s.
“This is an amazing record. It tells you everything about United,” Butt added.
“Everyone at the club plays a vital role and should be extremely proud of this milestone.”