The offer of voluntary resignation expires on Friday, March 14, the broadcaster said.
According to CBS, the US Department of Health employs more than 80,000 people.
Earlier, a similar offer of $25,000 in compensation in the event of voluntary dismissal was made to employees of the US Social Security Administration.
In late January, NBC reported that the Trump administration was offering 8-month severance pay to government employees who agreed to resign voluntarily, with up to 10% of federal officials expected to accept the offer, and this initiative would save the government billions of dollars. A senior administration official told the channel that 5-10% of federal employees were expected to be fired.