Highland Council has made the request to Rural Affairs Secretary Richard Lochhead after Wick, Helmsdale, Brora, Golspie, Embo, Portmahomack, Balintore, Cromarty, Rosemarkie and Nairn were affected by the bad weather.
Leader Drew Hendry told Mr Lochhead in a letter: "The storm surge caused extensive damage along the eastern coastline and our officials are carrying out detailed inspections to assess the nature of the damage.
"We have experienced significant damage to existing coastal defences which threatens the homes of many coastal communities. There has been extensive damage to harbours at Balintore and Portmahomack, as well as damage to a links golf courses and coastal footpaths.
"The detailed assessment has still to be completed. The initial estimate is that the overall cost of repairs will be significant."
Mr Hendry said he welcomed the minister's commitment to consider providing emergency financial assistance and would very much welcome the opportunity of an early meeting.
Meanwhile, flood warnings were removed from Scotland after days of heavy rain. On Monday, Environment Minister Paul Wheelhouse visited Stonehaven, which was badly hit..