Emergency services were called to the scene at about 11:00, when a green Vauxhall Corsa left the northbound carriageway.
A man in his 20s and a woman in her 30s have been taken to Ninewells Hospital in Dundee. The extent of their injuries is not yet known.
Crash investigations are under way and Police Scotland appealed for witnesses.
A man and woman have been injured after a car crashed off the A90 road near Stracathro on Sunday morning.