Dr Renjit Nair, 36, was accused by Lianne Sabin, 24, and Mark Smith, 27, of not fully examining their 17-day-old son Calum at Doclands Medical Centre, Preston, Lancashire, in 2009, the Daily Telegraph reported.
At the time, Calum was not feeding and was suffering with cold and sweating.
He died in hospital a day after being examined by Nair.
The GMC panel said Dr Nair had performed an examination of the sick child and had made a "true and accurate record" of the consultation, the report said.
