The two men visited early on Saturday and waited outside the Live Turtle & Tortoise Museum like eager visitors.
When staff of the museum inside the Chinese Garden opened its doors at 9am, the men went to the front desk and demanded to adopt a tortoise.
They claimed that the museum's website stated that visitors were able to do so, even though it did not.
When they were rejected, they paid the adult entry fee of $5 and went into the museum.
But when they left at 9.35am, they had taken more than just photographs.
They allegedly stole an endangered Indian star tortoise, which is estimated to cost about $2,000.
Their act was caught on the museum's closed-circuit television and the footage has been handed over to the police.
No workers were around to monitor the area at the time as they were still busy with the opening of the museum.
On regular days, there would be at least two employees keeping a lookout in the museum.
Museum owner Connie Tan, 43, told The New Paper: "We are not in it for the money, we just want to educate children (on the different types of tortoises and turtles). Please don't do this to me."