Someone inside the parlor called 9-1-1 to report the robbery in progress, and police arrived before the robbers could flee, Evers said.
The men holed up in the shop, which was surrounded by SWAT and K-9 units. Two of the three surrendered after a brief standoff, police said. Neither was found to be in possession of a gun, Evers said.
Officers continued their search for the third man but waited until daybreak to climb onto the roof - which has many levels, chimneys and places to hide - to decrease the risk of a surprise attack, police said.
"He was hiding pretty good up there," Evers said.
The man was apprehended, but was unarmed when taken into custody, police said.
Evers said that the third man may have discarded the weapons in one of the chimneys and ducts on the roof, and that police and dogs were searching for the firearms.
Police did not identify the suspects.
Investigators said they were trying to determine if the men were responsible for recent robberies at other massage parlors in the city.
Although massage parlors may not seem like typical hits for robbers, Evers said that because the shops deal mostly in cash and can sometimes cross the boundaries of a legal business, robbers consider it less likely that employees will phone police during a crime.
Lt. Charles Green, of the department's City-Wide Vice Squad, said the squad was familiar with the New World Spa Massage Parlor, but he declined to elaborate.
Green said he wasn't aware of patterns in recent massage-parlor robberies but that massage parlors have been targeted in the last eight years.