Officers were called to reports of a disturbance on Gordon Street around 9.45pm on Saturday.
Police said two men, aged 39, have since been arrested and charged in connection with the alleged incident.
Both men are due to appear at Glasgow Sheriff Court on Monday.
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A Police Scotland spokesperson said: “Around 9.45pm, on Saturday, 2 September, 2023, officers attended a disturbance involving two men on Gordon Street, Glasgow.
“A police officer was injured during the incident. He was taken to hospital and released after treatment.
“Two 39-year-old men were arrested and charged in connection with this incident and are due to appear at Glasgow Sheriff Court on Monday, 4 September.
“A report will be submitted to the Procurator Fiscal.”