Among the missing were Spain's Rafael Nadal, who cited an undisclosed muscle strain, and Switzerland's Stanislas Wawrinka, who suffered a serious knee injury Thursday in practice and was slated to undergo surgery Friday.
He was replaced by rookie Stephane Bohli in his scheduled match against David Ferrer, who won by scores of 3-6, 6-2, 6-2.
"I am fully behind my colleagues and have utmost faith in them," said Wawrinka, who estimated he will miss 10 to 12 weeks. "I also count on the support of the public in Geneva and promise to come back even stronger for the next tie."
The Swiss team also is playing without world No. 1 Roger Federer, who decided not to play because of fatigue from his heavy schedule.
The opening day ended with a 1-1 tie.