Uriel Landeros, 22, is charged with graffiti and criminal mischief felonies for allegedly spray-painting on "Woman in a Red Armchair" at an exhibit in Houston on June 13, 2012.
Each felony charge carries a sentence of two to 10 years in prison.
The vandalism was captured in a 24-second video taken by a bystander and posted on YouTube. The vandal left behind an image of a bullfighter, a bull and the word "conquista," which means "conquest" in Spanish.
Prosecutor John Lewis said Landeros - a U.S. citizen - fled to Mexico after the incident. He surrendered to authorities at the U.S.- Mexico border last week. State District Judge Vanessa
Velasquez agreed that Landeros posed a flight risk.
Landeros' attorney, Emily Detoto, said she intends to file a motion asking that his bond be reduced.
Landeros said little during the court hearing, giving only brief answers to Velasquez' questions.
He has, however, given several media interviews in which he admits he was the graffiti artist behind the damage to the Picasso. In videos posted to YouTube, Landeros says he didn't intend to destroy the painting but that his actions were an act of social and political defiance.
Vance Muse, a spokesman for the Menil Collection, said the painting is still being restored in the Menil's conservation lab, but the process is nearly complete and has been successful.
"To the naked eye, you and I would not know it had been touched," he said. "It is in very fine shape. We are very, very relieved."
The painting will be back on display sometime this year, Muse said.
Muse said the Menil has sought an estimate of the painting's value but that he deemed it "priceless." He also could not estimate the restoration costs. The felony charges against Landeros call for damages of from $20,000 to $100,000.
The Menil, which opened in 1987 and is free to the public, did not make sweeping changes to its security or how it displays paintings as a result of the vandalism, Muse said. The museum's
security measures include surveillance cameras and two dozen guards.
"No matter what you've got in terms of guards, cameras or alarms, it just takes one vandal to move very quickly to do it," Muse said.
The vandalism charges garnered Landeros national attention and in October a Houston art gallery raised the ire of the local art community by staging a show of his works.