Federer said he was aware that the blogger had recently issued an apology.
The 17-time Grand Slam champion has had heavy security surrounding him at all times since arriving in Shanghai.
"I felt fine" Federer said. "There was maybe one quick thought. I saw one of the bodyguards outside of the court. I thought, still around, obviously. I have bodyguards every time I play a match on a center court, which is normal.
"Once the match started, got underway, I never thought about it again."
Federer saved the one break point he faced and broke serve once in each set to secure his path to the third round. He'll next face 13th-seeded Stanislas Wawrinka.
"I thought it was a good match for me," Federer said. "Obviously not having been broken is a good thing early on in a tournament.
"You hope it sets a trend for more to come."
Second-seeded Novak Djokovic also advanced, beating Grigor Dimitrov of Bulgaria 6-3, 6-2.
Djokovic won the China Open in Beijing last week for his fourth title of the year and 32nd of his career. He has now won 66 matches this season, the most of any player on tour.
Djokovic didn't offer Dimitrov a break-point opportunity and never lost more than one point in any service game. He also served four games at love.
"Very pleased with my serving in Beijing and obviously the first match today," Djokovic said. "So that's something that I've been working on, obviously. Relying on the serve in today's tennis is a big advantage. So I try to get as many free points as possible. It helped me a lot to defeat my opponent."
If Djokovic wins in Shanghai and Federer loses before the quarterfinals, the Serb would reclaim the No. 1 ranking next week.
Andy Murray received a walkover into the third round on Wednesday following the withdrawal of Florian Mayer of Germany because of a rib injury.
"I went to the gym this morning in the hotel, and he was in the gym at the same time," Murray said. "I didn't know until 15, 20 minutes ago."
Murray is the two-time defending champion at the tournament with a 9-0 record after winning finals against David Ferrer last year and Federer in 2010. The third-ranked Briton also won the Olympic gold medal at the London Games and a title in Brisbane title earlier this year.
Fifth-seeded Jo-Wilfried Tsonga beat Benoit Paire 7-6 (7), 7-5 in an all-French match.
For the second straight day at the tournament, a match went to three tiebreaker sets. Marcos Baghdatis of Cyprus upset 12th-seeded Milos Raonic of Canada 7-6 (4), 6-7 (5), 7-6 (3).
Sam Querrey of the United States came from behind to beat 14th-seeded Kei Nishikori 2-6, 6-2, 6-4 in another second-round match.
Nishikori sought a medical timeout for a right ankle injury that he sustained last week.
"It's disappointing, but I was close to a win even with this injury," Nishikori said.