The overall World Cup leader, who was tipped for medal success ahead of the Games, hopes to recover in time for the 50K classical.
"I got a call saying Per has a cold, although he had no fever," Swedish team spokesman Jan Nordin said.
"He says he maybe already had this before the 30-kilometre race last week, which he didn't finish."
"He's not leaving the Games. We hope he can recover and come back for the 50-kilometre race next Saturday."
So far at the Olympics Elofsson has finished a disappointing fifth in the 15K classical and fourth in the pursuit.