Arn, the 2011 champion, fought harder than the scoreline suggested, but could not stop Radwanska getting her 2013 off to a solid start.
"The first match of the year is always hard, especially going from practicing indoors in the off-season to the conditions here," Radwanska said. "My opponent was very tough today, too. The score looks easy but the match was not easy - we had a lot of tight, long games. I really had to fight for every ball."
Second seed Julia Goerges also enjoyed a straight sets win, downing Anastasija Sevastova 6-3 6-4.
"It's always nice to get a win, and to get one in two sets is very nice," Goerges said. "I expected a tough match from Anastasija and I got it. I think it's much better when you get tough matches at the start of a tournament, so you can really try to show what you've been working on."
Britain's Heather Watson moved into the second round after opponent Sorana Cirstea was forced to pull out with illness. Fifth seed Cirstea had lost the first set when she called time on the match. Next up for the Brit is Kiki Bertens of the Netherlands.
Yaroslava Shvedova and Mona Barthel, seeded sixth and eighth respectively, won through, while Marina Erakovic and Romina Oprandi also booked second-round places.