Tunisia's Jabeur, who is ranked ninth in the world, was beaten by unseeded American Kenin in a gruelling match which lasted two hours and 17 minutes in the hot Rome sunshine.
Jabeur, who in 2022 became the first Arab and Tunisian player to win a WTA 1000 title, looked to be on the right track after reaching the quarter-finals in Madrid.
But she slumped to a poor defeat on Friday, continuing a dreadful season so far in which the 29-year-old has had to deal with a chronic knee injury resurfacing.
Jabeur has a losing record for the year, a far cry from the woman who looked like she had the world at her feet ahead of last year's Wimbledon final, which she lost in straight sets to unfancied Marketa Vondrousova after blasting through a series of Grand Slam champions.
World number 42 Kenin will face either Rebecca Sramkova or Katie Boulter in the third round.
Earlier fifth seed Maria Sakkari swept past qualifier Varvara Gracheva in straight sets, 6-2, 6-2.
Elena Rybakina was supposed to open her title defence against Romania's Irina-Camelia Begu but dropped out with an illness and was replaced by French lucky loser Oceane Dodin.
"I am disappointed to have to withdraw from Rome this year, but unfortunately I do not feel well enough to compete," world number four Rybakina said in a statement.
Djokovic begins bid
Top seed Djokovic takes on lucky loser Corentin Moutet in his opening match on centre court on Friday evening with a great chance to add to his six titles in Rome.
The 24-time Grand Slam winner has made no secret in the past that he loves playing in Italy and with a clutch of big names either out injured or struggling he will fancy his chances of a record-extending 41st Masters 1000 crown.
The Rome tournament, which runs until May 19, is missing two of its biggest stars with Italian world number two Jannik Sinner and third-ranked Carlos Alcaraz both withdrawing from the men's draw before the start.
Meanwhile clay court icon Rafael Nadal had a creaky start in the first round against qualifier Zizou Bergs on Thursday and is on the opposite side of the draw to his great rival, meaning the only way that the pair could face each other would be in an unlikely final.
One of Djokovic's potential threats, third seed Alexander Zverev, breezed into the third round with a 6-0, 6-4 win over Australia's Aleksandar Vukic.
This year Zverev has reached the semi-finals at the Australia Open and Miami and the quarters of Indian Wells and with some stellar absences he could find himself in the last four against Djokovic.
"It was a good start, especially with the first set because I came out firing there," said Zverev.
"I know I'm the sort of player who can lose to anyone, I've unfortunately done that in the past but I also know that I'm a player that once I do find my rhythm I can beat anyone and I hope this can be the week where I find it."
Home hope Lorenzo Musetti withdrew with a stomach bug and flu-like symptoms midway through his match with France's Terence Atmane.
World number 29 Musetti was a set and one game down when he gave up the ghost in his second-round match with unseeded Atmane, and joined Sinner and Matteo Berrettini as local favourites to retire from their home tournament.
