Rabe'e Ata Juma'a Alqaq, 24, had traveled to Houston to represent Jordan in the Genuine Cup, which features intellectually disabled athletes from 50 countries.
Campus police say he and his teammates had just settled into their dorms at Martel College around 9 p.m. Saturday.
Around 12 a.m. Sunday, police said Alqaq told his dormmates that he was going to do some exploring.
It was the last time anyone saw him.
Police say Alqaq's dormmates reported him missing around 2:30 p.m. Sunday.
"There were still some items in his room, so that's why it's kind of prompted us to believe that he's missing," Lt. Francisco Fernandez with the Rice University Police Department said.
Surveillance video shows Alqaq walking across campus wearing a light blue T-shirt and black pants.
A different camera picks him up at Entrance 23. He appears to be headed off campus but then turns around and heads in the other direction while glancing at what looks to be a phone.
"He does not know the area, doesn't know the city, new country, doesn't speak the language, the weather. All those things factor into everything, and yeah, reason for concern," Fernandez said.
Police say they've been unable to access his cell phone location data since they don't have the same working relationships with foreign cell service providers.
Investigators say they are working to access his social media accounts to see who he might have been communicating with in the hours leading to his disappearance.