This warning, which come's following the Defence Secretary's visit to Scandinavia, is the second one Mr Wallace has issued to Moscow in a week.
On Monday, Mr Wallace told an event in London that there would be “consequences” of any Russian aggression towards Ukraine, and Britain would “stand up to bullies”, no matter how far away the conflict.
Tensions on the Ukrainian border continue to be fraught, with the US suggesting Moscow is preparing for a “false-flag operation” in order to spark an incursion into neighbouring territory.
The new US intelligence was unveiled after little progress was made in talks between the Kremlin and Washington and its Western allies aimed at heading off the escalating crisis.
Foreign Secretary Liz Truss, appearing to back up the US intelligence, accused Russia of “waging a disinformation campaign intended to destabilise and justify an invasion” of Ukraine, and called on President Vladimir Putin to “de-escalate” the military presence.
Amid the stand-off, Ms Truss’ colleague, Defence Secretary Mr Wallace, met Nordic partners this week, including Finland which shares a border with Russia.
The Ministry of Defence (MoD) said he met with ministers in Sweden, Finland and Norway to discuss Russia’s continued aggression and military build-up on Ukraine’s border, with some 100,000 troops amassed at the divide.
Mr Wallace said: “The UK and our Nordic partners are united in our approach to upholding European security.
“My discussions this week have been directly about deepening bilateral relations, shared security and the consequences of Russian aggression towards Ukraine.
“Our discussions were clear that a Russian invasion of Ukraine would be a strategic mistake, violating the most basic freedoms and sovereignty.
“Britain and the Nordic countries have a long and shared history.
“Our European neighbours and allies remain vital partners as we work together to defend our common values, counter shared threats and build resilience in our neighbourhood, the UK will always stand with them.”
Similarly, Labour said the threats facing Ukraine must be met with “strength and solve” by Nato and Europe, with shadow defence secretary John Healey having visited the country this week.
The senior opposition MP said: “The Western allies must work hard to maintain their deterrent pressure on Russia and stand by Ukraine.”
Giving details of the Defence Secretary’s three-day visit, the MoD said that Mr Wallace met with his Swedish counterpart, defence minister Peter Hultqvist, before travelling to Finland to hold discussions with President Sauli Niinisto, foreign minister Pekka Haavisto and defence minister Antti Kaikkonen.
The third leg of his trip saw the Defence Secretary meet with his Norwegian counterpart Odd Roger Enoksen.