According to transport body Viasuisse a two kilometre tailback had built up by 10.30am which is expected to grow to nine or ten kilometres by Wednesday afternoon, reported news agencies.
By Thursday – Ascension day and a public holiday in much of the country – a two-hour wait is expected to access the tunnel.
Swiss federal railways (SBB) has laid on an extra 29 trains towards the south allowing for 46,000 extra seats.
Holidaymakers will enjoy summer temperatures across the country over the long weekend, with the mercury touching 30 degrees in some places.
In a statement MeteoNews forecast beautiful conditions and high temperatures for Ticino but said the weather nevertheless "wasn't worth" sitting in the Gotthard traffic jam for.