The play happened during Thursday's 2-1 Vancouver victory over the Coyotes.
Edler was assessed a five-minute major after running into Smith behind the net late in the second period.
Smith was injured on the play and finished the period but wasn't back in net for the third. He was replaced by Jason Labarbera.
Edler will miss games on Saturday at Los Angeles and Sunday at Colorado. He is eligible to return on Tuesday when the Canucks host the Columbus Blue Jackets.