Robyn Gardner, 35, was last seen on the Caribbean island on Aug. 2, said Ann Angela, spokeswoman for the Aruba prosecutor's office.
An American man who was traveling with Gardner was arrested Friday, Angela said.
"We suspect him of involvement in the disappearance of Ms. Gardner," she said.
Angela said she could only disclose the man's initials, G.V.G., due to the office's policies. The 50-year-old man was arrested as he was at an airport, about to leave the country, Angela said.
She said the man's role in Gardner's disappearance is under investigation, and detectives are still trying to determine whether Gardner is alive.
The Aruba Herald identified the suspect as Gary V. Giordano. Maryland records show he lives in Gaithersburg.
Giordano reported Gardner missing after she disappeared during a snorkeling trip, the Herald reported.
Giordano's Aruba lawyer, Michael Lopez, did not respond to calls for comment. Lopez told the Herald that he has advised Giordano to remain silent because he already spoken extensively with police.
Gardner's trip to Aruba came as a surprise to her boyfriend, Richard Forester, who said he thought Gardner was going to Florida to see her family.
Gardner had an apartment in Frederick but had been living with Forester in Bethesda since January, he said. She worked as a patient coordinator at a dental practice, but recently lost her job.
Forester said he last heard from Gardner in a Facebook message on Aug. 2. He said he tried to contact her for three days before learning Friday that she had been reported missing.
"I suspect something went wrong," he said.
Forester said he knew of Giordano, but didn't know the extent of Gardner's relationship with him.
Angela said a judge on Sunday ordered the suspect to stay in custody for eight days, and will determine at another hearing this weekend whether he should be released or remain detained.