Gasol will be sidelined at least three weeks.
Lakers spokesman John Black told the Los Angeles Times that according to Gasol's agent, Arn Tellem, there were no issues with the surgery, which took place immediately after the injury occurred Monday.
The Spanish basketball federation said Tuesday that Gasol injured the finger while blocking a shot during the workout in preparation for the European Championships.
He will wear a splint for 20 days, but the federation did not say if he will play in the championships, which start Sept. 7 in Poland.
Gasol, however, hopes to do so.
"I want to be with my teammates and fight for the championship," the Spanish news agency Efe quoted him as saying at a news conference in Cadiz. "I don't see why I would have to drop out.
Gasol was a key part of the Lakers' championship this past season, averaging 18.9 points and 9.6 rebounds during the regular season. Black said Gasol had spoken with the Lakers' trainer, and the team was trying to get in touch with the surgeon who operated on Gasol.
"I have explained the situation to the Lakers, and they have the results," Gasol said. "They aren't pleased I am injured but I don't think they'll put obstacles in my way."
Spain is the reigning world champion but lost to Russia in the final of the 2007 European Championship. Spain won the silver medal at the 2008 Beijing Olympics, at which the United States won gold.
Information from Reuters and The Associated Press was used in this report.