The clearance is a major milestone for Neuralink, which wants to use brain implants to cure a range of conditions including obesity, autism, depression and schizophrenia.
Musk, who founded Neuralink in 2016, made headlines last year when he said he was so confident in the devices' safety that he would be willing to implant them in his own children.
According to a report in Reuters, Neuralink had hoped to receive approval to implant its device in 10 patients.
But following safety concerns raised by the US regulator, the company is reportedly negotiating a lower number of patients.
In a tweet Neuralink said the FDA clearance "represents an important first step that will one day allow our technology to help many people."
The FDA approval comes after another reported breakthrough in brain-implant technology after a Dutch man paralyzed in a biking accident regained the ability to stand and walk with the help of implants placed in his brain and spinal cord.
In a first for science, the implants are able to “capture the thoughts” of Gert-Jan Oskam, 40, connecting his intentions to his physical movements, the scientists behind the technology said.
The implants are able to translate Oskam’s thoughts “into a stimulation of the spinal cord to re-establish voluntary movement,” said Gregoire Courtine, a co-author of the study and a neuroscientist at the Swiss Federal Institute of Technology, said.
With the implants, Oskam – who has been paralyzed since 2011 – can reportedly walk about 330 feet at once and stand for several minutes without using his hands for support.