The walkout was in protest at what workers say are low staffing levels on the company's planes. By 6pm on Tuesday SAS had cancelled 24 flights to and from Copenhagen.
SAS could not put a figure on how many Swedish travellers were affected by the strike, but Copenhagen Kastrup Airport serves large parts of southern Sweden, including Malmö. It also provides intercontinental connections for passengers from Stockholm and Gothenburg.
Four of the flights cancelled were linking the Danish capital with Stockholm Arlanda and Gothenburg Landvetter.
"We have lots of direct international flights and those passengers do not need to worry," said Monica Hultberg, spokeswoman for SAS Sweden.
"Unfortunately lots of other passengers are going to be hit by delays and cancellations," she said.
The strike, which breaks the terms of the collective agreement for SAS cabin crew, broke out at 2:15pm.
The company is trying to book as many passengers as possible on other flights. SAS Denmark said that passengers hit by cancellations could also apply for refunds.
All passengers were being advised to follow information on Copenhagen Airport's homepage. SAS Denmark warned that more flights could be cancelled during the evening. Half of SAS flights between Sweden and Denmark have Danish crew and therefore risk being cancelled.