The findings by Strathclyde University's Fraser of Allander Institute (FAI) found that the planned job losses in the two sectors could also inflict a £325 million blow to the Scottish economy.
In the FAI report, which was commissioned by the Unite Scotland trade union, 1,500 direct job losses are estimated in civil aviation, from companies including Menzies Aviation and Swissport - with a knock-on effect for another 830 jobs.
Following aerospace engineering redundancy consultations and voluntary severance schemes for 1,225 roles at Rolls Royce, GE Caledonian, Spirit Aerosystems and Wyman Gordon, the report also forecasts the ultimate loss of 2,530 jobs across Scotland.
Scotland's Gross Value Added (GVA) could suffer an overall loss of approximately £140 million because of the impact on the civil aviation industry, in addition to a £185 million decrease from the aerospace engineering sector, the FAI estimates.
Director of the Fraser of Allander Institute, Graeme Roy, said: "The full effects of the economic crisis from the Covid-19 shutdown are sadly only beginning to crystalise.
"The job losses announced already in key parts of our economy - including aviation and engineering - have the potential to be a damaging blow to Scotland's long-term economic prospects."
Unite Scotland is now warning the Scottish and UK Governments that both sectors "could be on the brink of terminal decline" and is calling for additional support packages for the industries.
Describing the report's findings as "eye-watering", Unite's Scottish secretary Pat Rafferty said: "Over the course of several months there is an estimated loss to the Scottish economy of £320 million and nearly 5,000 direct and indirect jobs are on the brink of being lost forever.
"This is the gravity of the situation facing both sectors and - make no mistake about this - both are on the cusp of terminal decline without immediate intervention from both the UK and Scottish Governments.
"It's essential that the Governments get all the key stakeholders in these sectors around the table immediately so that we can protect and save as many highly-skilled jobs as possible."
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