The failed scheme could cost taxpayers £400m.
On Thursday, the whistleblower said it was evident there were "opportunities for fraud" in the scheme.
She said she contacted Arlene Foster, the then enterprise minister, in 2013 to warn about the issue.
Speaking on BBC's The View, Simon Hamilton expressed regret that the woman's complaint was not taken seriously by Stormont civil servants.
"I want to thank [her] for her contribution and to apologise to her for the fact that her complaint was not taken seriously by government. It was taken seriously, however, by Arlene Foster, who passed the information on to her officials, and that's absolutely the right thing."
He defended the first minister, saying she has "shown leadership" and has nothing to hide.
"The communication from the whistleblower was not specific about what the alleged abuse of the scheme was and it was appropriately passed on by Arlene to her officials, who were tasked to investigate it," he said.
"It was they who didn't take the complaint seriously."
1, 946 applications were approved under the non-domestic Renewable Heat Incentive scheme - a 98% approval rate.
984 of them were received in just three months - September, October and November 2015 - after officials announced plans to cut the subsidy but before the change took effect.
The assembly's Public Accounts Committee was told that a subsequent independent audit had found issues at half the 300 installations inspected.
14 of these fell into the most serious category where fraud was suspected.
Payments to five of these 14 sites have been suspended.
He added that "no recommendation was brought forward to bring in cost control measures and the issue hadn't actually crystalised during her time in the department".
"People are asking should she resign. She absolutely should not resign as she has done nothing wrong," he said.
"Arlene, like me, sees the importance of getting to grips with this incredibly serious issue. I'm not going to sit here and say anything other than that this is a shocking situation and one that needs to be dealt with."
Mr Hamilton said he and the first minister are working on a plan that will reduce the cost to Northern Ireland taxpayers.
"This issue is the number one priority for my department and I hope to bring forward the details of that plan early in the new year."
The Northern Ireland economy minister has said he wants to apologise to a whistleblower who raised concerns about the financial cost of the failed renewable heat incentive scheme.