Snodgrass, who scored the winner when Scotland beat Croatia 1-0 in June, was given leave by Strachan to attend the birth of his daughter Leonie.
"I'm absolutely buzzing after the birth of our baby," the Norwich midfielder told the Scottish FA's official website.
"I managed to train at the club last week but I think the adrenaline of fatherhood alone will get me through it.
"I'm looking forward to training tomorrow and I would like to thank the manager for being so understanding."
Scotland are still waiting for their first home win of the campaign but Snodgrass is looking for a rousing farewell to continue the momentum into preparations for the Euro 2016 qualifiers next year.
"It is important we finish as high up the table as we can and really give the crowd at Hampden something to cheer," he added.
"We don't want to finish the group without a home win and after the momentum we have built up it would be great to finish the campaign with another positive result that we can take into the preparations for the European Championship qualification campaign."