"The first troop trains with Russian servicemen who are part of the [forces] began to arrive in Belarus," Valeriy Revenko, head of the ministry's international military co-operation department, wrote on Twitter.
"The relocation will take several days. The total number will be a little less than 9,000 people."
More information would be provided at a briefing for military attaches, he said.
Belarusian President Alexander Lukashenko said last week that his troops would be posted with Russian soldiers near the Ukrainian border, after what he said were threats from Ukraine and the West.
The announcement follows footage shared by the ministry on Saturday night of what it said were Russian servicemen arriving in Belarus.
Images from the ministry showed soldiers welcomed by women wearing traditional costumes and handing out bread and salt.
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The ministry’s press service said the decision for the regional grouping of troops “was made and is being implemented solely in the interests of strengthening the protection and defence of the state border of the Union state on the territory of Belarus”.
“This decision was caused by the ongoing activity in the border areas," it said on its Telegram channel.
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Last Monday, Mr Lukashenko claimed Ukraine was plotting to attack his country and announced the joint force with Moscow.
The Russian posting raised fears that Belarusian troops could join Moscow's forces in their offensive in Ukraine.
On Friday Mr Lukashenko said that the Belarusian army and its 70,000 troops would constitute the "base" of this joint force.
He did not specify how many Russian soldiers were expected to join.
"We do not need to ask for 10,000 to 15,000 people from Russia," Mr Lukashenko said. "They have other issues over there, as you know."
Minsk said Tuesday that the contingent was "purely defensive".
Ukrainian President Volodymyr Zelenskyy at a G7 meeting last Tuesday accused Russia of "trying to directly draw Belarus into this war".
Mr Zelenskyy called for an international observers mission to be placed on the Ukraine-Belarus border.
Mr Lukashenko told NBC last Friday night that his country supported Russia but "we did not kill anyone and we are not going to kill anyone".
"No one asked us to get involved in this operation, not Russia in this case, and we do not intend to get involved," he said.
Mr Lukashenko said his country was "treating Russians and Ukrainians, feeding Russians and Ukrainians", and welcoming Ukrainian refugees.
He is an ally of Russian President Vladimir Putin and allowed Belarusian territory to be used by Moscow's troops to launch an invasion of Ukraine in February.
But Belarusian armed forces have up to now not taken part in the offensive. Belarus relies financially and politically on Russia.