"He came up here swinging the bat and swinging hot," Gonzalez said. "I'm surprised he hasn't burned his hands, already."
In 21 games in June, Weeks hit .309 with seven doubles, three triples, six RBIs and six stolen bases, which was good enough to finish tied atop voting for the award with Twins outfielder Ben Revere. Weeks also had seven multi-hit games for the month.
Weeks, who described his first month in the Majors as a "whirlwind," was hitting .299 entering Tuesday's game against the Mariners, with a .330 on-base percentage.
"Not bad for his first month," A's manager Bob Melvin said. "We've seen what he brings to the table. ... He's been as advertised, and we expect big things out of him."
"It feels good," Weeks said. "Just to get any accolade this early in your Major League career, it's all positive, right now. It's something I never really thought about getting. I was just out here trying to help the team win and play well. I'm glad to know it's been noticed."
Meanwhile, Gonzalez earned AL Player of the Week honors for the first time in his career, after going 2-0 with a 0.60 ERA and a Major League-leading 16 strikeouts in wins over the D-backs and his hometown Marlins. Gonzalez shared the award with Toronto's Jose Bautista.
"It's an exciting award," said Gonzalez, who was also named an All-Star for the first time in his career on Sunday. "I'd like to continue to try to keep my head down and receive more awards like that.
"When we get Florida guys representing, it's even more exciting."