This is possible on normal Linux machines with RTC wake alarm:
$ sudo sh -c "echo 0 > /sys/class/rtc/rtc0/wakealarm"
$ sudo sh -c "echo `date '+%s' -d '+ 3 minutes'` > /sys/class/rtc/rtc0/wakealarm"
I have never tried this on Android, and if it does work, I'd imagine it requires rooting your device. Maybe that'd be good enough for your use case.
As @CommonsWare mentioned, some manufactures seem to support this as a setting. I'm not sure if they have an API, but that might also be worth researching. One of them seems to be Samsung.