The city says the investigation stems from an allegation made against the chief.
It's related to an off-duty relationship Balderrama is said to have had with a non-city employee.
City officials say they first became aware of the allegation from Balderrama himself in February.
The statement reads, in part:
The City commenced an administrative investigation utilizing an independent investigator retained by the City Attorney's Office to determine if the police chief violated department policy. The investigation is in the review process.
The city says that Balderrama will remain on duty in his position as chief while the investigation is finalized.
Hours after the accusation was made public, Chief Balderama posted on social media, writing, "We will be okay."
A photo of the Bible verse was also attached with the post, reading: "Never will I leave you, never will I foresake you. Hebrews 13:5."
Action News spoke to law enforcement analyst and former LA County Sheriff's sergeant Bruce Thomas about the investigation.
"Typically the city doesn't get involved," said Thomas. "This is kind of a unique case, and I don't know why."
Thomas said even when the investigation is finished, it's likely not much information will be released to the public.
"As the chief is with every officer in the State of California, they're covered by the Peace Officers Bill of Rights," said Thomas.
"Investigations are confidential and not open to freedom of press or Freedom of Information Act. Even the discipline, whichever is handed out, is covered also."
The news of the accusation comes as Balderrama has served as the city's police chief for three-and-a-half years.
He joined the department in 2021 from Oklahoma City, where he served as deputy police chief.
Balderrama made history by becoming Fresno's first Latino police chief.
Stay with Action News for the latest updates on this developing story.
For news updates, follow Gabe Ferris on Facebook, Twitter and Instagram.
For news updates, follow Ana Torrea on Facebook, Twitter and Instagram.