The blast happened at 22:35 BST on Monday at the end of a concert by US singer Ariana Grande.
Police said the lone male attacker, who died in the blast, detonated an improvised explosive device.
Relatives are using social media to hunt for missing loved ones, and an emergency number, 0161 856 9400, has been set up.
Sixty ambulances attended the incident and those wounded are now being treated at six hospitals around the city.
Chief Constable Ian Hopkins said it was "the most horrific incident" Greater Manchester had ever faced.
He said the "fast-moving investigation" was now working to establish whether the attacker "was acting alone or as part of a network".