The group have vowed to support AJ (centre)
He had initially entered a 30-day programme but has decided to continue treatment on the advice of doctors.
His delayed return means the band will have to postpone an extra 10 shows on their US tour, on top of dates they have already rescheduled.
Shows in Washington and Los Angeles have been cancelled altogether because of scheduling difficulties.
Band member Kevin Richardson said: "AJ's initial treatment is going very well.
"His doctors have suggested it would be in AJ's best interest to take an additional two weeks in transitional care."
Fellow member Nick Carter added: "We truly want to thank our fans for standing with us through this.
"And we know that it will be worth the wait for them to see the five of us back on stage."
McLean, 23, entered an unknown clinic on 9 July, suffering from clinical depression and anxiety, as well as alcoholism.
Support
At the time, the rest of the Backstreet Boys backed his decision to seek help.
A statement on the group's website says: "AJ is our friend and our brother and we whole-heartedly support him during this difficult time. Fortunately, AJ has realized he can't solve his problems by himself."
The band believe McLean's recent problems are due in part to the recent death of his grandmother.
The group's tour was originally planned to conclude in Vancouver on 7 August but it will now conclude on 20 October.
The tour is to promote their latest album Black and Blue, which has sold around six million copies worldwide.