Wimbledon champion Garbine Muguruza congratulated Serena Williams on the birth of her baby girl and jokingly hopes the newborn does not follow in the footsteps of her illustrious mother.

American tennis legend Williams, 35, welcomed her first child into the world on Friday - a baby girl with fiance Alexis Ohanian at St Mary's Medical Center in West Palm Beach, Florida.

The 23-time grand slam champion and former world number one has been away from the WTA Tour preparing for the birth of her baby.

Asked about the newest addition to the Williams family, Muguruza joked: "Baby girl? Well, I hope she doesn't play tennis [smiling].

"Well, I'm very happy for her. I mean, such a good moment, I'm sure. Well, there it is, in her arms, I'm sure, also."

Spanish third seed Muguruza was speaking after she stormed into the last 16 of the US Open on Friday.

Muguruza made light work of Magdalena Rybarikova 6-1 6-1 in a match lasting just 61 minutes at Flushing Meadows.

Standing in the way of Muguruza and the quarter-finals is two-time Wimbledon winner Petra Kvitova.

"I feel I have improved a lot as a tennis player," Muguruza reflected on her performances compared to last year. "You know, the summer has been great, and I'm playing a lot of matches. So the fact that I played so much matches gives me, you know, gives me pretty good confidence."

Muguruza added: "Playing somebody in the third round that you played in the semi-finals [at Wimbledon], it's a little bit tough match, and I just learned off what I did there. And basically I do a lot [with] my game. Go forward, try to hit some big shots and big serves.

"Today went my way at the start of the match almost."