Segregated lanes are common in countries such as the Netherlands and Denmark, but there are few others in Scotland, like the first part of the Bears Way between Glasgow and Milngavie.
However, the Milngavie scheme has proved controversial with both drivers and cyclists, with claims that its layout is dangerous.
Mr Mackay said the “Community Links Plus” contest would provide as-yet unspecified funding to encourage local authorities to design “exemplar” segregated lanes on roads.
They are especially aimed at people making more short trips by bike, most of which are made by car.
The winning schemes are due to be announced in a year’s time and built over the following two years.
Mr Mackay said: “This competition aims to deliver high-profile, continental-style infrastructure which will improve safety while also encouraging less confident cyclists to make day-to-day journeys by bike.
“I would encourage as many local authorities as possible to submit proposals for schemes that will benefit their residents and visitors alike.”
The Scottish Government’s Transport Scotland agency added: “The amount of funding available will be subject to confirmation of final budgets for future years and the proposals received, with local authorities and their partners expected to at least match the Scottish Government’s investment.”
John Lauder, national director of cycle path developers Sustrans Scotland, said: “The best investment any government can make is to help people choose to travel in ways that benefit their health and wellbeing, so we are delighted at this new development which will help people to use a bicycle for an every-day short trip.”
Keith Irving, chief executive of Scottish Government-funded co-ordinating body Cycling Scotland, said: “Further investment in quality cycling infrastructure and promotion is essential for encouraging anyone, anywhere to cycle.”