The midfielder scored one of Rangers’ two Scottish Cup winning goals in the win over Hearts last weekend.
However, an calf problem means the 30-year-old will miss out in midweek as Steve Clarke's side bid to secure a play-off final place against Wales. Jack is expected to be sidelined for all of Scotland's June fixtures.
Clarke has opted to bring in the uncapped Allan Campbell as cover. The former Motherwell midfielder has enjoyed a productive season with Luton Town, who were denied a place in this weekend's Championship playoff final after a narrow semi-final defeat to Huddersfield Town.
It is the latest cruel blow for Jack, who missed last summer’s European Championship finals as well as the first half of the new season due to a calf injury.
He returned in time to help Rangers reach the Europa League final against Eintracht Frankfurt and came on as substitute to play a significant role as the Ibrox side lifted the Scottish Cup four days later.
Meanwhile, Clarke is determined to give Jack’s former Ibrox teammate Nathan Patterson every chance to feature against Ukraine.
The manager is preparing to make a judgment call on the wing-back’s physical condition after assessing him in training.
The 20-year-old last played a top-level game in March when he started Scotland’s 2-2 friendly draw with Austria.
He has been instrumental in Scotland's recent good run and would be expected to be a certain starter.
But he has struggled to break into the Everton side after making a £12 million switch from Rangers in January and then was sidelined by injury as he prepared to make his Premier League debut.
Frank Lampard replaced Rafa Benitez shortly after Patterson moved south and the player has made just one start for the new manager - against non league Boreham Wood in the FA Cup, when he was replaced at half-time.
Clarke revealed that Lampard planned to hand Patterson his first league start in April but the player picked up an ankle injury on the eve of the game in training and has not featured since.
“Well, he is not going to be match fit because he hasn’t played,” the manager conceded. “I think the last time he played was for us. He played for us in the March games. He lasted about an hour - 65 minutes in the first and an hour in the second.
“He was unfortunate because I had a chat with Frank Lampard after those games and Nathan was going back to start for Everton against West Ham and he got injured the day before the game which put him out for the rest of the season. He was unlucky from that point of view. That was disappointing and obviously for us as well.
“I will just gauge it when he comes in," added Clarke. "I think when he joins up with us it will be his first chance to train with a group of players.
“He has been working on his own and it’s always different when you go into group training and you start to work. We will just have to look at Nathan and we will make a judgement on that as we see him in the training.”