The former England midfielder, 43, took over at the Championship side in October 2022 for his first role in management.
He guided the team to a play-off finish in 2022-23 but they have missed out on the top six in the past two campaigns.
Carrick’s assistants Jonathan Woodgate and his brother Graeme Carrick have also left the club.
Boro spent much of the 2024-25 season challenging for a play-off spot but one win in their final six matches proved to be costly.
They stayed in the hunt for a top-six place until the final game of the season but defeat at Coventry saw them finish 10th.
His departure means that 17 of last season’s 24 Championship teams have changed manager since August last year.
Ends