Some of the islands' communications and power have now been restored, but the internet may be out for a while longer because of damage to an undersea cable.
After the eruption, Tonga's main island was blanketed in ash and its western coastline is said to be devastated.
"We're getting sketchy information, but it looks like the cable has been cut," the Southern Cross Cable Network's networks director Dean Veverka told the AFP news agency.
"It could take up to two weeks to get it repaired. The nearest cable-laying vessel is in Port Moresby," he added, referring to the Papua New Guinea capital, more than 4,000 km (2,500 miles) from Tonga.
The underwater volcano erupted on Saturday, sending a plume of ash into the sky and triggering warnings of 1.2m (4ft) waves reaching Tonga.
The eruption was so loud it could be heard in New Zealand, some 2,383km (1,481 miles) from Tonga.
Hours later, Tonga's internet and phone lines went down, making the island's 105,000 residents almost entirely unreachable.
Phone and internet communications are extremely limited, while the situation in some coastal areas remains unknown.
New Zealand and Australia are sending surveillance flights to assess the extent of the damage.
They were also assisting with satellite calls, Tonga's deputy head of mission in Australia, Curtis Tu'ihalangingie, told Reuters by phone.
There are approximately 428 submarine cables, running 1.1 million km around the globe providing internet and communications links.