Roger Gower, 37, who was working for the Friedkin Conservation Fund, had been tracking elephant poachers.
The Fund said the arrests were the suspected gunman and others involved in the poaching operation, plus members of the criminal gang behind the illegal guns and ivory smuggling.
Further arrests were likely, it added.
Fund chairman Dan Friedkin said in a statement: "We are confident that the Tanzanian authorities will investigate and prosecute those involved to the absolute full extent of the law.
"By bringing these individuals to justice, it will honour Roger's memory. We also fervently hope that it will mark the turning point in Tanzania in the fight to protect elephants and our wildlife heritage."
Mr Gower was on a joint operation with the Tanzanian wildlife authorities to track down and arrest active elephant poachers when he came under fire on 29 January. Three elephant carcasses had been found in the area.
The incident happened in Maswa Game Reserve, which borders the Serengeti National Park in northern Tanzania.
Mr Gower managed to land his helicopter but died from his wounds before he could be rescued.
Three people were arrested on 1 February.
He was originally from Birmingham and worked in London before moving to East Africa to work as a helicopter pilot.
Mr Gower's brother Max said he was proud of how he had managed to land the helicopter and allow his passenger, a friend and colleague, to get out.
He said his sibling quit his job as an accountant the day he qualified as a pilot so he could go to work with the two things he enjoyed the most - flying and animals.
The Gower family have invited donations to a fund established in Roger's memory that will contribute towards anti-poaching efforts in Tanzania.
Five people have now been arrested over the killing of a British pilot whose helicopter was shot down by poachers in Tanzania, his employer has said.