The tweet, which has now been deleted, was a retweet of a post that showed Ukrainian president Volodymyr Zelensky signing an application membership for Ukraine to be in the European Union.
The SNP MSP also said she was “delighted” for the country, which has suffered attacks ordered by Russian president Vladimir Putin.
It comes as Freedom Square in central Kharkiv, Ukraine's second city, has been hit by a Russian strike, causing a huge explosion.
Ms Thomson was formerly the MP for Edinburgh West from 2015 to 2017, and since 2021 has been the MSP for Falkirk East.
On Monday, President Zelensky asked the European Union to allow Ukraine to join the bloc under a fast-track procedure.
At just before 4pm on Monday, the official Twitter account of the Ukrainian’s legislature posted a picture of President Zelensky signing the application, saying it was an “historic moment”.
Around an hour later, Ms Thomson then retweeted it and added the message: “Delighted for Ukraine. It’s [sic] just goes to show what political will can achieve. Remember this Scotland!”
She later deleted the tweet and apologised around 8pm on the same night.
Ms Thomson said: “I noted and then tweeted something earlier that was insensitive regarding Ukraine. Like everyone, my first thoughts are sympathy for the people there. Apologies if I offended anyone.”
The apology comes after people took to Twitter to criticise the Falkirk MSP for her “crass” tweet.
Kirsteen Sullivan, West Lothian Labour councillor, replied on Twitter: "I don’t think the Ukrainian people are ‘delighted’ as they try to survive, hour by hour, not knowing if they will see loved ones again.
"What a crass thing to tweet to try make a cheap political point, there’s no ‘if’ about it."
Conservative MSP Stephen Kerr posted: “We've got...Michelle Thomson modelling a break-up of the UK on Putin's invasion of Ukraine.
"This is not normal behaviour for a political party.”