Galit Nakash is to take a DNA test to determine if the girl is her biological daughter, following a court hearing.
If the results are negative, authorities say they will return the child to Sri Lanka straight away.
Ms Nakash was stopped when airport officials found she had used another child's passport to leave Sri Lanka.
She says she gave birth at a hospital in Sri Lanka during a business trip but that her visa application for the baby, named Tahel, was turned down.
On Tuesday a court in Tel Aviv accepted her request to undergo a DNA test in Israel.
Ms Nakash's lawyer, Matan Hodorov, said his client and the one-year-old child are being moved to a facility at Ayalon prison in Ramle until the results of the test are known on Friday.
Mr Hodorov said Ms Nakash, 49, turned down an Israeli request to take a DNA test while she was in Sri Lanka because she did not trust the process there.
He said when Ms Nakash, who runs an export business and comes from Tel Aviv, re-entered Israel, the passport she used for Tahel carried the name of a different child.
However he said he was "confident the DNA test will prove Galit is the mother [of Tahel].
"We have all the correct medical documents from the hospital in Sri Lanka where she was born," he told the BBC.
The Israeli foreign ministry said Ms Nakash was denied a visa for Tahel because officials had doubts about her story.
"There were a few indications which raised a certain amount of suspicion," spokesman Emmanuel Nahshon said. "That is why we did not allow the child and Galit to enter the State of Israel.
"It doesn't mean she is wrong but we have a legal duty to check it out. If the DNA tests show she's the mother then that's wonderful and the problem is over. If not, the child will immediately be sent back to where she came from, as required under the Hague Convention [on child abduction]," Mr Nahshon said.
"Nobody is trying to take the child away or create a tragedy, but the circumstances are extremely suspicious."

27 May 2016 Last updated at 19:43 BST
Here's his Africa news round-up in 90 seconds.

Media playback is unsupported on your device
10 December 2014 Last updated at 07:08 GMT
Nasa astronaut Commander Chris Hadfield dropped into Newsround's mission control to answer kids questions, taste our finest space food and sing a cracking space lullaby.
Here's your chance to watch it again.
An Israeli woman and a baby who returned from Sri Lanka have been kept at Tel Aviv airport since Saturday amid questions over the child's origins.
[NEXT_CONCEPT]
Satirist Ikenna Azuike from What's Up Africa is worrying about the tomato shortage in Nigeria, celebrating improved life expectancy and reflecting on presidential breakdowns.
[NEXT_CONCEPT]
It has been a fantastic year for space exploration this year, from landing the Rosetta space probe on a comet, to testing out rockets that could take astronauts to Mars.