The 23-year-old Radwanska took just more than 70 minutes to overcome Arn, the 2011 champion now ranked 114, who entered the main draw as a lucky loser after being beaten in the last round of qualifying.
Radwanska controlled the match from the baseline, with occasional forays to the net, unsettling Arn with her strong forehand and off-balance backhand.
Arn was the second former champion to lose in the first round after 2012 champ Zheng Jie of China was beaten in straight sets on Monday.
"I really felt good on court, but there were a lot of tight, long games," Radwanska said. "The score looks easy, but the match was not that easy. I had to fight for every ball to the end of the match."
Second-seeded Julia Goerges of Germany beat Latvian qualifier Anastasija Sevastova 6-3, 6-4 in the last match of the first round. Goerges took the first set in just more than 30 minutes but had to fight hard to take the second with a single service break.
Earlier, sixth-seeded Yaroslava Shvedova of Kazakhstan beat Lara Arruabarrena-Vecino of Spain 6-3, 6-2. Shvedova served six aces and had five double-faults but still overcame her Spanish opponent in 71 minutes.
Fifth-seeded Sorana Cirstea of Romania became the third seeded player to exit the tournament, after seventh-seeded Christina McHale and fourth-seeded Jie, when she retired in the second set of her match against Britain's Heather Watson.
Cirstea received medical attention after Watson took the first set 6-3, then was forced to retire because of a viral illness.