The child was taken to the Royal Hospital for Sick Children in Glasgow, from a house in Cambuslang, following the alleged incident on 21 December.
His condition was described as serious.
The Crown Office said that David McMullan, 32, appeared at Glasgow Sheriff Court last Friday where he made no plea or declaration and was remanded in custody.
Mr McMullan was charged with attempted murder and assault to severe injury, permanent impairment and danger to life.
A man has appeared in court charged with the attempted murder of a two-year-old boy in South Lanarkshire.