The devastating eruption in mid-January damaged an undersea telecommunications cable, which experts have said could take a month to repair.
National Party MP Dr Shane Reti wrote a letter to Musk, who also produces electric cars under the Tesla brand, asking for help to provide his Starlink satellite technology to the Pacific country.
The technology uses satellites to deliver internet access to remote locations around the world.
Musk replied offering to assist Tonga, asking on Twitter whether Tonga authorities could inform him whether Starlink terminals were needed.
The Fiji Broadcasting Corporation, FBC News, reports that the team from SpaceX are now in Fiji to work on an internet gateway for the Kingdom of Tonga.
Minister for Communications Aiyaz Sayed-Khaiyum confirmed the news to FBC News, saying the engineers from SpaceX will establish and operate a temporary ground station in Fiji for six months.
"The Space Exploration Technologies Corporation (Space X) had applied for a temporary emergency telecommunications license on the 20th of Jan, the sole purpose of this license is to provide an internet gateway," Sayed-Khaiyum told FBC News.
"Space X and FINTEL are currently, however, in commercial negotiations to co-locate the earth station and connect to Fiji's internet gateway."
SpaceX has also reportedly shown interest in providing internet services in Fiji.
The Herald has approached Sayed-Khaiyum for comment.
Reti said it was "wonderful news".
"I am just really pleased for Tonga and all the Pacific that they will be getting modern telecommunications."
Reti said he had been in contact with the Tongan consul and Minister for Pacific Peoples, Aupito William Sio, who were pleased to hear the news.
