In line with the policy of its parent Wal-Mart, the chain pledged earlier this year to move all wild-caught supplies of fresh and frozen seafood to MSC-accredited species by 2010.
But Asda said: "Waitrose and M&S have mopped up all the MSC fish and no one can get their hands on enough."
Only 6% of all seafood caught globally for human consumption is certified or at some stage within the programme. However, 32% of the world's prime white fish catch is now at some stage of certification.
But with most major supermarkets now stocking MSC lines, Asda faces competition for supply.
MSC chief exec Rupert Howes was surprised by Asda's claim. "There are 3.5 million tonnes of seafood in the programme and 500 MSC lines globally. We've overcome the no market-no supply phenomenon."