Scotland cap Burke, 19, left Forest to join RB Leipzig in a deal that made him the most expensive Scottish player.
"It's a massive step," said McGovern, a club ambassador for Forest.
"He's got masses of potential. He has to be consistent and he has to get better at one or two of the things that he's not so good at."
Burke's move to the Bundesliga came after just 31 appearances for Forest, during which time he scored six goals.
"He's an impact player with fantastic pace," said McGovern, who played all his club football in England and played at Under-23 level for Scotland.
"I think he might even give Usain Bolt a run for his money.
"You need to be able to have an end product to that pace and he's been scoring one or two goals for the first team."
Unlike England, Northern Ireland, Republic of Ireland and Wales, Scotland missed out on Euro 2016 with the Gareth Bale-inspired Welsh team reaching the semi-finals.
But McGovern tempered comparison between Burke and Real Madrid's Bale, saying: "Gareth Bale wasn't playing for Real Madrid at 19 years of age and being outstanding for Wales in international competitions.
"If £13m is the fee for someone who's played a few games then obviously it's quite unusual but the transfer fees have gone right through the ceiling anyway so you should never be surprised with anything in football.
"It is an awful lot of money and it will be well spent if he realises his potential. He's got a good chance of becoming a very, very good player.
"The other thing about him going abroad is that perhaps, in some ways, it might benefit him because the thing he's got to keep away from is too much publicity and then perhaps starting to believe that publicity.
"Football can be a cruel game."
Meanwhile, James McFadden, who won 48 caps for Scotland between 2002 and 2010, believes the move to Germany will benefit both the player and the national squad.
"He'll learn a new culture and develop in a good way, hopefully, for Scotland," said Motherwell player-assistant manager McFadden, 33.
"Going over to a different country and learning a new way of playing the game will be great for his development.
"He's got a great physique and he looks as though he's got all the attributes to become a real top player. The fact that he's made the move at such a young age will tell you all you need to know about him.
"[RB Leipzig] will be hoping to challenge for the [Bundesliga] title because of the ambitions they've got. When players are doing well in Germany, Bayern Munich will snap them up, so that's got to be the next aim for him."
Former Nottingham Forest player John McGovern has cautioned against placing too much expectation on Oliver Burke following his £13m move to Germany.