According to a Swedish police statement, the dead are a man and a woman.
A man has been arrested on suspicion of murder.
IKEA spokeswoman Anna Pilkrona-Godden said that the Erikslund shopping centre containing the store had been closed.
Vasteras is about 70 miles west of the capital Stockholm.
“We found a man and a woman who had knife injuries and who later died of their wounds,” police said.
The victims were “ordinary shoppers” in the kitchen accessory section, Mattias Johansson, the store manager, told local newspaper VLT.
Several ambulances were at the scene and the area was cordoned off by police, eyewitnesses told local media.
“Our thoughts are with those affected,” said Anna Pilkrona-Godden.
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