They were arrested on Tuesday two days after the boy was taken to hospital with cardiac arrest.
The pair, from Wolverhampton, appeared before magistrates on Thursday.
They are charged with causing grievous bodily harm, engaging in sexual activity with a child under 13 and causing or allowing a child to suffer serious physical harm.
The baby is in New Cross Hospital in Wolverhampton and remains in a critical condition, police said.
The man, aged 22, was remanded in custody to appear at Wolverhampton Crown Court on January 21.
The 18-year-old woman has been released on bail to appear alongside her co-accused.
Two other women, aged 46 and 32, have been arrested and released on bail.
A man and woman have appeared in court accused of a series of offences against a baby who is critically ill.