The First Minister told Holyrood that organisers of larger events would “be expected to carry out a reasonable number of checks” for spectators attending.
The new certification rules come into force on October 1 and will apply to all stadia and arenas with capacity over 10,000.
The Scottish football joint response group has been in discussion over the proposals and while optimistic from the First Minister’s statements the group is seeking to iron out further details before the October 1 date the rule becomes law.
A spokesman said: “We warmly welcome the indications from the First Minister this afternoon that spot checks look likely to form the basis of vaccine certification at major events.
“We have been in detailed discussions with Scottish Government officials in the past few days as we seek to develop a workable and proportionate methodology.
“There remain a number of aspects which require to be finalised but we are hopeful that our positive talks will bear fruit and that Scottish football will continue to play a prominent role in reducing the impact of the virus.”
The group and SPFL chief Neil Doncaster had previously warned the deadline, at the end of this month, could pose difficulties if a blanket check of all covid certification was required for games at high-capacity stadia such as Murrayfield, Ibrox, Hampden and Celtic Park.
Hearts’ game at Tynecastle against Motherwell on October 2 is set to be the first game impacted by the law change.