The world number four, who is making his first appearance at the tournament since 2011, earned a convincing 6-1 6-2 victory over the Czech on Wednesday.
"I'm a bit surprised how well it went," Federer told the ATP's official website. "Then again, it's hard to serve through the opponent. I was able to get a lot of returns back into play. On clay, when you have the upper hand from the baseline, it's kind of hard to get out of it.
"I think that's kind of how it was for Radek today. I had a good start to both sets, then I was solid on my own service games. The next thing you know, you're in the lead and you can hit freely. It was clearly a good match to start my clay-court campaign."
Federer will now take on Lukas Rosol for a place in the quarter-finals.