Sosefina Amoa, 26, accepted a plea agreement for voluntary manslaughter, punishable by up to 30 years in prison.
A prosecutor has said she will seek a four to 10-year prison term.
A lawyer for Amoa said the Samoan woman smothered the infant in her room at the Little Sisters of the Poor convent but did so out of panic and shock after a difficult delivery.
She put her hand over the infant's mouth to "quiet the baby so she could figure out what she was going to do", lawyer Judith Pipe said.
Amoa is said to have arrived in the US from Samoa on 5 October 2013 to begin a five-month programme to become a member of the convent.
She gave birth to son Joseph in her room on 10 October.
Prosecutor Cynthia Wright told the Washington court Amoa was standing when the infant was born and that he fell, hitting the floor before he was smothered.
Amoa later cleaned her room and showed the infant to a sister at the convent the following day, saying she had found the child outside.
The unnamed nun allegedly found the child cold and not breathing and took the body in a bag to a local hospital along with Amoa, court documents said.
A trainee Catholic nun has pleaded guilty to killing her newborn infant in a convent in Washington DC in October.