In a statement to parliament, it was confirmed a debate and vote will take place at Holyrood next week regarding the plans.
If agreed, certificates will be introduced in limited settings later this month once all adults have been given the opportunity to be vaccinated. They would be used for nightclubs and adult entertainment venues, unseated indoor live events with more than 500 people, unseated outdoor live events with more than 4,000 people and any event which has more than 10,000 people.
With both Hearts and Hibs having sold more than 10,000 season tickets it would mean supporters would need to have had both doses to watch their team in action if the vote is passed. Other clubs most impacted in Scottish football include Aberdeen, Celtic and Rangers, plus the Scotland national team for World Cup qualifiers at Hampden Park.
The Joint Response Group has questioned the timing of the announcement and noted the lack of “appropriate IT infrastructure in place”.
It hopes to organise a meeting with the Scottish Government to discuss the plans further ahead of any potential rollout.
A statement released by the JRG said: "Scottish football is committed to the ongoing collective effort to eradicate the virus and continues to adhere to the strictest protocols even after restrictions were lifted across society.
“Indeed, on Monday the National Clinical Director, Professor Jason Leitch, gave a presentation to players and clubs on the clinical facts behind vaccination, to expedite the roll-out within the game.
“We have today raised concerns on the considerable unintended consequences of implementing a certification process without sufficient time or appropriate IT infrastructure in place.
“We will endeavour to establish full details in the coming days but stress the need to ensure a practical and workable solution for member clubs, their staff and supporters; in particular season ticket holders who bought their tickets in good faith and on the understanding they would be allowed back into the stadium when restrictions were lifted.
“We ask ministers to carefully consider the unintended consequences of certification, especially in such a short timeframe, and request a meeting with Scottish Government to discuss the matter and its implications for clubs prior to a parliamentary vote.”
SPFL chief executive Neil Doncaster told BBC Scotland of his surprise about the certificates and has put the game in the country “on the back foot”.
The First Minister believes the implementation would help control the spread of Covid-19.
More than 4 million people have received a first dose and nearly 3.7million with both doses.
"Many of the events and venues that are covered by the certification scheme are important – they matter to our economy, and to our cultural and social life,” she said.
"That's why we want to enable them to stay open safely – but they are not essential services.
"And the nature of them - which involves bringing many people together in relatively small areas – does mean that, despite their very best efforts, they can contribute significantly to the spread of the virus."