Mattek-Sands, ranked 48, upset the world number five 7-5, 6-2 in just over 90 minutes to disrupt Radwanska's lead-up to next week's Australian Open in Melbourne.
Radwanska's defeat was the first time since 1998 that the women's titleholder has lost her opening match in Sydney.
"She was really playing aggressive today. It didn't matter if it was my first serve, second serve, or anything, she was really going 100 percent for every ball," Radwanska said.
Former Wimbledon champion Petra Kvitova is the highest seed left in the draw after ousting American Christina McHale for the loss of just one game.
Also Read
Radwanska, who will now head to Melbourne ahead of the Open, said she did not think the early loss would upset her preparations.
"I had a lot of good matches last week (in the Hopman Cup)," she said. "It's not like I'm playing bad. I'm not worried about that. I just think it's not my day."
The former Wimbledon runner-up has not won a match or even a set since last October, after losing all three of her round-robin encounters at the season-ending WTA championships in straight sets.