Zinke tweeted the photo before speaking to the Western Governors Association at Mount Rushmore, South Dakota.
Zinke later apologized and re-posted the photo with "Make America Great Again" blacked out, saying he had not realized it could be viewed as a political slogan.
In March, the U.S. Office of Special Counsel sent updated guidance on the federal Hatch Act, which prohibits federal employees from engaging in political activity while on duty.
The guidance says employees may not wear, display or distribute items with the slogan "Make America Great Again" while on duty or in the workplace.
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Interior Secretary Ryan Zinke has deleted a photo of himself wearing socks with President Donald Trump's face and the slogan "Make America Great Again" after multiple groups said he was violating federal law.