Anja Mittag had put 2003 and 2007 champions Germany ahead after just six minutes with her fourth goal following her hat-trick in their opening 10-0 whipping of Ivory Coast.
But midfielder Mjelde equalised for 1995 winners Norway with a stunning free kick past former world player of the year Nadine Angerer in the Germany goal after 61 minutes.
The Germans next play Thailand who came from a goal down to keep their hopes of advancing alive with a 3-2 win over fellow newcomers Ivory Coast.
Germany coach Silvia Neid admitted her side had nearly paid heavily for letting their guard down after dominating early against the 11th-ranked Scandinavians.
“We just didn't play as well in the second half – and then Norway gained hope,” said Neid.
The result leaves Germany and Norway topping Group B with four points.
Thailand are third with three points with Ivory Coast bottom with none.
“The end result was fair, but we were lucky – (Germany) could have killed this game in the first half,” said Norway coach Even Pellerud.
In the final round of group games on Monday, Germany play Thailand in Winnipeg and Norway take on the Ivory Coast in Moncton.