Martin was granted his release Monday from Michael Waltrip Racing to join SHS. He will drive the No. 14 this weekend at Bristol and in 11 other races.
Dillon will race Oct. 20 at Talladega. Dillon filled in for Stewart on Sunday at Michigan and finished 14th. Stewart broke his right leg in a sprint car crash Aug. 5 at Southern Iowa Speedway.
"Obviously, I'm disappointed to be out," Stewart said in a statement. "But the team is in very good hands with Mark Martin and Austin Dillon. Mark is someone I've looked up to my entire career and I have a tremendous amount of respect for him. Austin is a great young talent, and he showed that Sunday at Michigan."
Greg Zipadelli, competition director at Stewart-Haas Racing, said Stewart needed to focus on his health and be ready to return next season.
Brian Vickers will now drive the No. 55 Toyota for MWR in 12 of the final 13 races. He was originally scheduled to drive just three more times. Michael Waltrip will race the No. 55 at Talladega as previously scheduled.
Waltrip said Martin achieved all of the goals both he and the team set when he began a 24-race schedule in the No. 55 in 2012.