The match will serve as preparation for World Cup qualifiers against Wales and Serbia the following month.
Scotland last played Estonia in May 2004 with James McFadden getting the only goal. Their last trip to Aberdeen was for a 3-0 friendly win over the Faroe Islands in November 2010.
Estonia are likely to feature Motherwell striker Henrik Ojamaa in their squad.
Scotland manager Craig Levein, whose team beat Australia 3-1 in midweek, said: "It is important that we continue to take the national team throughout the country and I am sure our huge support in the north east of Scotland will turn up in numbers for the Estonia match at Pittodrie.
"Like our recent victory against Australia, the Estonians will provide a tough and relevant challenge at the midway point of our FIFA World Cup qualifying campaign.
"The Estonians have improved markedly in the last two years. They reached the play-offs for UEFA Euro 2012 against Republic of Ireland, and they will provide a good test.
"The performance and result against Australia - a team ranked 22 places above us in the FIFA rankings - have given us a tremendous boost ahead of our opening qualifying group matches against Serbia and Macedonia next month.
"We will strive to build on the positives from midweek in the double-header and I would like to thank our supporters for demonstrating their loyalty and commitment by renewing their Scotland Supporters Club memberships and buying so many tickets already for the two matches at Hampden Park next month."