The 17-year-olds were approached by a group of about nine youths in the Trongate at about 2230 BST on Saturday.
It is understood they suffered stab wounds. They were both taken to the Glasgow Royal Infirmary.
The suspects are described as white and aged between 16 and 18. Strathclyde Police said the incident was being treated as racially motivated.
It is believed one of the injured youths was released from hospital after treatment for a head wound.
The other, who was detained overnight, is in a stable condition and is being treated for a back injury.
Det Sgt Sandy Johnston, from Stewart Street police station, said: "I would urge anyone who may have been in the area at the time and who may have seen the suspects, or indeed to anyone who may have information to contact us."
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