Firefighters were able to contain the fire using a ladder truck to battle the flames.
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The well-known restaurant is housed in Houston's historic Third Ward along Almeda Road.
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No injuries were reported in the fire, but what caused it remains unclear.
A few hours after, the owner, Nakia Holmes sent out a statement saying the fire has not directly impacted the business and that they are open.
"Last night, a small fire occurred at our off-site warehouse, not at the Turkey Leg Hut restaurant itself. We are relieved to report that, thanks to the swift and heroic efforts of the Houston Fire Department, the situation was quickly brought under control with no injuries and no impact on our restaurant's operations. We are deeply grateful to the firefighters and first responders for their dedication and quick action, which prevented any major damage. Their bravery ensures safety and minimal disruption, not just for us but for the entire community. We also want to extend our heartfelt thanks to our community for your concern and support during this incident. It's your support that uplifts us and reinforces why we do what we do every day. Turkey Leg Hut is open and we warmly invite everyone to join us for a meal. We remain as committed as ever to providing a safe, welcoming environment and delivering the delicious, comforting meals you've come to love".
The Houston staple filed for Chapter 11 bankruptcy last month, according to Holmes.
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Court records show the business owes about $4.7 million to creditors, including nearly $2 million in state tax revenue.
Holmes posted on Instagram that the move was to "reposition and strengthen the company."