The incidents come as EU accuses Belarus of helping thousands of asylum seekers and refugees cross into the bloc via Latvia, Lithuania and Poland since the summer.
Three refugees from Iraq and Syria have been beaten and robbed on the outskirts of a Polish town near the Belarus border.
One of the three, an Iraqi man, was taken to hospital after being struck on the head by one of the thieves with a metal pole near Hajnowka, one of the refugees and a charity helping them said on Friday.
A Syrian man who had crossed the border with the Iraqi man and his wife said they were attacked by three people, one of whom had a broken bottle.
"We asked them for water but... they attacked us," said the Syrian, who declined to be named, speaking throug h an interpreter from the Grupa Granica (Border Group), a non-governmental organisation.
"We didn't think it was a racist attack, more like a robbery. They beat us to find where the money was. We didn't want to say," he said.
The thieves stole 7,500 dollars (6,600 euros).
The incident happened on Thursday.
The border guard service on Friday said that two Iraqi nationals and one Syrian had been detained.
The three were spotted by volunteers from Grupa Granica who provided them with hot tea and soup.
Marysia Zlonkiewicz from Grupa Granica said the Iraqi man was "going in and out of consciousness" when the volunteers found him.
She said she was concerned that the refugees would be sent back across the border to Belarus.
Thousands of refugess – most of them from the Middle East – have crossed or attempted to cross from Belarus into the eastern EU states of Latvia, Lithuania and Poland since the summer.
The West has accused the Belarusian regime of engineering the flow of refugees in retaliation against European Union sanctions.
The refugess say they are being pushed across the border by Belarusian forces and back a gain by Polish authorities, leaving many stranded for weeks on end in dire conditions along the border.