The museum, which has been in operation for 11 years, has had 1.5 million visitors.
Liz Minyard, president of the museum's board, tells The Dallas Morning News, "This was not an easy decision to make."
The museum will stay open through this month.
Museum spokeswoman Haley Curry says the museum, like many institutions, had faced decreasing revenue during the economic downturn.
In 2009, the latest year for which records are available, the museum reported a $1.3 million deficit, after $2.6 million in expenses.
Curry says that the museum's collection, most of which has been loaned to it, will be returned to its original owners.