Rogers had to retire hurt on 49 on the fourth morning of the match.
Australia team doctor Peter Brukner said: "The initial scans have cleared him of any serious damage.
"It appears the most likely diagnosis is a delayed ear problem related to being struck on day two."
Rogers signalled to the dressing room after the second over of the fourth day at Lord's before slumping to his knees. He was given medical attention then helped off the field.
The 37-year-old did not field as Australia dismissed England for 103 to complete a resounding 405-run victory and tie the five-Test series at 1-1.
He was hit on the helmet by James Anderson's bouncer in his side's first innings, but continued batting to make a Test-best 173.