The men have been on hunger strike for 12 days in protest of their deportation orders, Swedish news agency Tidningarnas Telegrambyra reported.
The men, who are at an asylum-seekers' residence in Boden, appealed previous rulings by the Swedish Migration Board not to grant them asylum. The board said it won't reopen the application cases of eight of the men.
"We understand that people who are waiting for a ruling or who have had their asylum application denied are in a very difficult situation," said the Migration Board Director of Operations Mikael Ribbenvik.
"It is important to understand that we have an asylum process in Sweden where the Migration Board's decision can be appealed in a regular Swedish court," he added.
Three of the hunger strikers have been admitted to the hospital in critical condition, Red Cross representatives said.