Without giving details of the nature or origin of the threats, the statement from FBI spokeswoman Jacqueline Maguire said the investigators were taking the threats "seriously."
Bergdahl was was handed over to US forces in Afghanistan last weekend in exchange for the transfer of five senior Taliban leaders held by the United States.
The swap has unleashed a firestorm of criticism, in part because of allegations the soldier was only captured by insurgents after deserting his post.
"We are aware of the threats and are working with our local law enforcement partners to investigate," Maquire said.
"As always, we take these types of threats seriously," she added.
Bergdahl's hometown of Hailey, Idaho has also experienced a backlash over their support for him, according to media reports.
A massive town celebration planned for June 28 was cancelled over security concerns, USA Today reported.
Shopkeepers and town and county officials said since Bergdahl's release, and following media reports of the town cheering his safe return, the town has received angry phone calls and emails, the newspaper said.
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