Passenger train operator SJ says traffic between Stockholm and Gothenburg as well as Oslo and Stockholm has been cancelled until at least 2 pm Saturday.
Travel between Stockholm and Nyköping is expected to resume at noon and trains between Gothenburg and Karlstad will being running at 6 pm.
Dan Olofsson, a spokesman for the company, tells Radio Sweden that Helga's high winds brought down trees and overhead wires along the tracks. He says most traffic is running on schedule though there are a few delays affecting other lines.
"We had to take the decision to cancel the trains because it was too big of a risk to run the trains or buses instead of the trains because of the bad weather," Olofsson says.
He says the company is offering refunds to affected travelers and apologized for the inconvenience.
Power company Vattenfall reported about 7,400 customers without power late Saturday morning in southern Sweden, down from a peak of 55,000 households without power on Friday evening. Utility companies Eon and Ellevio had a combined outage of roughly 8,000 households.
Overall the storm caused few injuries. One person was hurt by scaffolding blown down by strong winds in Gothenburg and news agency TT reports that a firefighter was hit by a falling tree in Södertälje Municipality, just south of Stockholm.