European football's yearly showpiece is due to be held in St Petersburg on 28 May, but the match could now be moved to another host city due to the Ukraine crisis.
UEFA, European football's governing body, is widely reported to be considering switching the final's venue from St Petersburg's Gazprom Arena.
Ms Truss added to the pressure on UEFA to act as she urged the West to "disassociate ourselves" from the regime of Mr Putin.
The Russian president this week ordered troops to enter two regions of Ukraine after declaring them to be "independent" states.
Asked by Sky News' Kay Burley whether this year's final should be held in Russia, the foreign secretary replied: "No it shouldn't be. I'm very clear it shouldn't be."
Ms Truss added: "The way that Russia is behaving we should not be in any way seen to condone that behaviour, we must condemn it absolutely.
"We are in real danger at present of a full-scale invasion on Ukraine and all we can do to disassociate ourselves from Russia and this appalling regime we should do now."
The Gazprom Arena is named after the majority Russian state-owned energy giant for sponsorship reasons.
Gazprom is also a Champions League sponsor.
Four English sides - Manchester City, Liverpool, Chelsea and Manchester United - remain in this year's Champions League and have a chance of reaching the final.
Ms Truss confirmed that Prime Minister Boris Johnson "misspoke" when he told MPs on Tuesday that Chelsea owner Roman Abramovich had previously been sanctioned by the UK.
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