Baker, son of former Bucks assistant Carl who served alongside Paul Carden until his sacking earlier this season - was signed earlier in the campaign on a non contract deal.
But after a small number of appearances has now left the club on a permanent basis - as has goalkeeper Louie Grey, who was signed as cover for the then injured Luke Pilling.
Elsewhere, Kade Craig who was signed last month on loan from Shrewsbury Town on a short team deal has returned to Salop.
Craig has been unavailable in recent weeks following a shoulder injury - and has returned to the League One club following the conclusion of his loan.
The club also provided an update on injuries to Jason Oswell, Liam Nolan, Jordan Piggott and Devarn Green - and have confirmed Brendon Daniels will missed the next three games following his red card against Kidderminster Harriers.
In a statement, the Bucks also said boss Kevin Wilkin and his staff are working hard to strengthen their squad ahead of Saturday's clash with Banbury.
The statement read: "We can confirm Louis Baker has left the club. Louis who had been signed on non-Contract has left the football club on a permanent basis. We can also confirm Goalkeeper Louis Grey has also left the club. Louis was signed on non-contract to cover the injury to Luke Pilling. We would like to wish both Louis and Louis all the best in the future.
Injuries to Jason Oswell, Liam Nolan, Jordan Piggott and Devarn Green continue to be assessed on a weekly basis and we hope to have them back as soon as possible.
"Brendon Daniels will now be unavailable for the next three fixtures following his sending off against Kidderminster Harriers.
"Boss Kevin Wilkin and his staff are continuing to work as hard as possible to strengthen the squad and we hope to have some further developments this week ahead of Saturday’s fixture at home to Banbury."