The furor is so far contained to Norway, which is one partner to the Scandinavian venture.
"There have been strong reactions and I'm sure it will explode in Sweden once it gets out," said Stig Lundsbacken, chair of the union Verkstedsklubben, to the newspaper VG.
Lundsbakken said the move was unacceptable if it was not also extended to blue-collar workers.
SAS responded on Friday and said "a very limited number of key persons" had been offered the bonus.
"This limited group is intended to find ways to cut expenses within the company, which might in fact mean that they themselves lose their jobs," SAS press spokeswoman Malin Selander wrote in an email to the TT news agency.
Swedish white-collar union Unionen was despite this upset.
"I am very upset. We were forced to accept worse working conditions that affect the employees' lives. To then find out the company is losing money on the other end is unacceptable," chairman Sven Cahier told TT.
He has heard that 18 top managers are getting between three and six additional monthly wages, which adds up to 15 million kronor ($2.3 million).
Cahier said two of them had already quit.
"So the bonuses aren't having the proposed effect," he told TT.
Story continues below…
SAS came under heavy fire for strong-arm tactics resulting in unions accepting massive wage cuts in late 2012 which are widely believed to have saved the airline from going under.
“As an SAS stakeholder, the Swedish state has pulled the rug from under the Swedish model despite the government saying it is in favour of it,” Unionen spokeswoman Louise Gerdemo Holmgren told The Local in November.