Professor McKay was professor of economics at Glasgow Caledonian University, and a leading figure in making the case for women in the labour market, helping to shape government policy in this area.
Speaking at First Minister's Questions at Holyrood, Mr Salmond said: "Ailsa, as we all know, was a leading voice in campaigning for gender equality, not simply through her work, but as a founding member of the Scottish Women's Budget Group.
"This week, as we look forward to International Women's Day, above all I think it is important that we note her astonishing contribution as a feminist economist, both in arguing the case for women into work, and in being the principal author and arguer for many years for the transformation of childcare that will make that possible."
Professor McKay was a founding member of both the Scottish Women's Budget Group and the European Gender Budget Network, and a member of International Association for Feminist Economics.
Professor Pamela Gillies, principal and vice-chancellor of Glasgow Caledonian University, also paid tribute to her contribution.
She said: "In her far too early death, Scotland has lost an important force for good, the university has lost a greatly valued, committed and intellectually vibrant colleague, and I have lost a dear friend. Our thoughts are with her partner Jim and the family at this difficult time."
Grahame Smith, Scottish Trades Union Congress (STUC) general secretary, said: "With the tragically early passing of Professor Ailsa McKay, the STUC has lost a great friend, colleague and counsel. Ailsa always had time to help and support any project which sought to improve the lives of working people and she made a particularly special contribution to the work of our Women's Committee and Close the Gap project.
"The thoughts of all at the STUC are with Ailsa's partner Jim, her children Annie and Rory and her many, many friends and colleagues at Glasgow Caledonian and across Scottish pubic life."