Pete Wishart, the party’s constitution spokesman at Westminster, said another vote on Scotland’s future should be delayed until the “full impact” of Brexit is being felt.
The Perth and North Perthshire MP argued that the SNP needed time to come up with a “credible post-Brexit vision” for an independent Scotland.
Ms Sturgeon postponed her plans for another referendum after the SNP lost 21 seats at the general election, but is still committed to holding a vote after the terms of the UK’s deal with the EU are clear.
However, Mr Wishart said Prime Minister Theresa May’s decision to seek a two-year Brexit transition period starting in 2019 meant that the First Minister would be wiser to wait until after 2021.
“Timing is everything and we must seek the optimal time for success, carefully assessing opportunity against risk. We must also have an unquestionable mandate,” he wrote in an article for a Scottish daily newspaper.
“This means contesting the next Scottish election with a clear commitment to revisit our constitutional future with a reference to allow Scotland to consider its position when Brexit finally concludes.”
He continued: “With transitional arrangements in place, it is likely that the full impact of Brexit will start to become apparent just as we start to contest the 2021 election.
“We therefore have to seek a renewed mandate in 2021 and have the courage of our convictions to fight the next Scottish election on securing a renewed referendum mandate.”
Last week Ms Sturgeon admitted she did not know when she would call another referendum, saying she was wary about adding to the uncertainty people are already feeling.
Mr Wishart said the delay he was proposing would give the SNP time to create a new case for leaving the UK, which he described as “Independence 2.0”.
The SNP’s Growth Commission, which has been given the task of exploring the possible financial arrangements and currency of an independent Scotland, is set to publish its recommendations over the next few months.
The Scottish Conservatives called for Ms Sturgeon to take Mr Wishart’s advice and rule out calling another referendum during the current Parliament.
Murdo Fraser MSP said: “Pete Wishart’s comments will only add to the confusion over what the SNP’s policy is on a referendum.
“The trouble is that, while the SNP continues to dither, investment decisions will be put off and more uncertainty will be cast over Scotland’s future.
“Nicola Sturgeon has shown a total failure of leadership on this matter over the summer. She now has a responsibility to take control and make it clear to her party that a referendum is off the table for good.”
Scottish Labour’s business manager James Kelly said: “The SNP should be focused on delivering better jobs, schools and hospitals for Scotland, not plotting about when is the best time to hold another referendum that the majority of Scots don’t want.”
An SNP spokeswoman said: “The only uncertainty facing business and investors right now is being caused by the Tories’ shambolic Brexit plans, which threaten Scottish jobs, investment and living standards.”