Tongan community leader Melino Maka said Jones was approached after dozens of people within the Tongan and wider Pasifika community in New Zealand reached out, wanting to know how they could help.
"A lot of people are being told send donations only - in money. But some people just won't do that. Our people like to give something or do something.
"They can see a container of food and know that it will go straight to people there. A lot of people are wanting to send containers [of supplies] after hearing from back home, but it's expensive.''
The Matson group will put up 12 20ft (6m) containers in total, free of charge. The containers will go to various parts of Tonga and help villages in different districts; particularly on the islands of Tongatapu and 'Eua, which were hit the hardest.
The first round of containers is estimated to arrive on March 15 or 16.
Maka's group - the NZ Tongan Hahake Community - will offer its supplies, in six containers, to help people in 23 villages on the eastern side of Tongatapu.
Sir Michael stressed that Matson was only one of several companies and business folk who had come forward to help donate or provide discounted services for the Tongan community's relief efforts.
"For us, we're just happy to do this because it's the least we can do. We really value the relationship with the community."
Sir Michael, who holds the Samoan chiefly title La'auli, acknowledged that the Pasifika community in New Zealand was incredibly close and was also very much supported by Kiwis from all different backgrounds.
"It's not just the Tongan community hurting. We feel the pain too - we're all part of the family, especially as Pacific Islanders. When one hurts, we all feel it too."
He said they had been overwhelmed to hear of the situation in Tonga, where there remains a worry over food supplies, water issues as well as rebuilding homes destroyed or damaged in the cyclone.
"We've heard of the destruction - that 40 per cent of house have been damaged. Even small damages still means damage. This [rebuild] will take a long time.''