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.

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McIlroy, 27, is one of 20 players to have withdrawn from next month's Games, citing fears about the Zika virus.
He said he would not watch the Olympic golf on television.
Speaking after Thursday's first round at The Open, McIlroy said: "I decided to stop dancing around the issue and tell everyone what I thought."
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The four-time major winner added: "I've thought about Olympics and golf for the last seven years and this is just how I feel.
"Some people don't like it, I get that; but it's my opinion.
"I don't think anyone can blame me for being too honest. It was seven years of trying to give the politically correct answer and finally I just cracked."
On Tuesday, the Northern Irishman said: "I'll probably watch the Olympics, but I'm not sure golf will be one of the events I'll watch."
Asked which events he would watch, McIlroy replied: "Probably track and field, swimming, diving, the stuff that matters."
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Those comments received criticism from English squash player Laura Massaro, whose sport is not included in the Olympics.
She called McIlroy's comments "unacceptable" and said he had shown a "lack of appreciation for how the Olympics can transcend an individual sport".
However, McIlroy, who is six shots off the lead after the first day of the Open, has tried to elaborate more on his comment that he "didn't get into golf to try to grow the game".
Find out how to get into golf with our special guide.
"I feel I've done my bit to grow the game," added the world number four. "It's not like I'm uninterested and golf is a great vehicle to instil values in kids.
"I'm an ambassador for the PGA Junior League and I've used my success in golf in a very positive way."
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A trainee Catholic nun has pleaded guilty to killing her newborn infant in a convent in Washington DC in October.
[NEXT_CONCEPT]
Former world number one Rory McIlroy has remained defiant in the face of criticism over his controversial views on golf at the 2016 Rio Olympics.