The 20-year-old left-back joined the League One club on a season-long loan last week but was forced off with the injury in Tuesday's League Cup win at Luton.
"He probably won't feature for a few weeks," Swindon manager Mark Cooper told BBC Wiltshire.
"We think he's got a grade one medial strain. We're waiting for a scan result from Liverpool but he certainly won't be able to feature for a few games."
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