The Lithuanian border guards did not see the migrant, who was lying on the ground, because of flashlights pointed at them by Belarus' officers, it said.
Giedrius Misutis, the SBGS spokesman, told BNS that the incident took place when Lithuania's border guards were throwing migrants' belongings from Lithuanian territory into Belarus to prevent them from setting up a camp.
"The Belarusians kept shining their flashlights at our officers all the time; there was a small distance between them," he said. "The handler was temporarily blinded at that time and his dog grabbed the sleeping bag. The handler immediately pulled the dog away when he saw that someone was moving."
The migrant was not injured, because the dog bit him "through a thick sleeping bag, through clothes", according to the spokesman.
"They were there all night; [there was] no ambulance. They stayed near the border and stood there quietly," he said. "In the morning, they started moving along the border, accompanied by Belarusian officers."
Belarus' border guards have released video footage that shows several Lithuanian border guards, one of whom is holding a service dog on a leash, trying to push the migrants, who were lying on the ground in sleeping bags, across the border.
In the footage, several migrants are seen getting up when the Lithuanian officers with the dog approach, but one of them continues to lie down and is bitten on the leg by the Lithuanian border guard's service dog.
Lithuanian border guards on Wednesday published video footage from the same place, but it did not include the moment when the migrant was bitten by the dog. However, it showed a Belarusian officer with a flashlight on.
The SBGS said on Wednesday morning that it was a group of 13 adult men who said they were Iraqis.
The migrants told the border guards that they had been detained by Belarusian officials after arriving in Minsk and forcibly taken to the border with Lithuania.
They said they wanted to get to the border with Poland and then travel further to Western Europe, according to the SBGS.