Medical personnel were rushed into the East Room after Smith fainted while Biden called for year-round support for women's sports. Smith, who was standing in the risers behind the podium, slunk downward and was helped off the stage as the ceremony was halted for about 10 minutes.
"It's a lot of standing," Biden said. "I apologize. It's OK. It's happened lots of times."
LSU coach Kim Mulkey said Smith was fine as personnel wheeled her out, and Smith later told NOLA.com that she was "way better" after being released from the White House's care.
"I'm great, better -- way better than earlier," said Smith, who made her way back to the team's hotel. "I don't quite remember how everything happened. I just remember waking up pretty scared. The last thing I remember is telling one of my coaches, 'Hey, I think I'm going to pass out.'"
LSU said in a statement that Smith felt overheated, nauseous and thought she might faint. The school also said Smith would undergo further evaluation in Baton Rouge.
Joked Mulkey: "As you can see, we leave our mark where we go."
Biden signed an old-fashioned leather basketball for Smith, writing: "Sa'Myah -- it was wonderful (to) have you at the White House. You are the best. /Joe Biden 5-26-23"
Having LSU to the White House marked a thawing of earlier tensions between the team and the administration. After the championship game, first lady Jill Biden had suggested also inviting runners-up Iowa to the White House in what would've been a break from tradition.
At the time, LSU star forward Angel Reese, who averaged 23 points per game this past season, said she was "hurt" by the plan, but she was on hand Friday to offer a hug to Jill Biden and present her with a commemorative jersey.
"Folks, we witnessed history," President Biden said. "In this team, we saw hope, we saw pride and we saw purpose. It matters."
Since the passage of Title IX in 1972, Biden said more than half of all college students are women, and there are now 10 times more female athletes in college and high school. He said most sports stories are still about men, and that that needs to change.
"We need to support women sports, not just during the championship run but during the entire year," Biden said.
The Connecticut men's championship team also visited the White House for its own celebration on Friday, with Biden switching from a purple tie to a blue tie to welcome the Huskies.
"Congratulations to the whole UConn Nation," Biden said.
Reuters and The Associated Press contributed to this report.