Nessa, 28, was killed last Friday as she walked the short distance from her home in southeast London to a local pub where she was planning to meet friends. She never arrived.
Her body was discovered in a nearby park the following day, sparking a murder investigation.
“Sabina’s family have been informed of this significant development and they continue to be supported by specialist officers,” Detective Chief Inspector Neil John said, according to the statement.
The Met previously arrested two other men — a 40 year-old and another 38-year-old — who have since been released under investigation.
The latest arrest comes days after authorities released CCTV footage showing a man walking in Pegler Square shortly before Nessa’s killing.
Catherine, the Duchess of Cambridge, also paid tribute to Nessa in a Twitter post on Friday, saying she was “saddened by the loss of another innocent young woman on our streets.”
“My thoughts are with Sabina’s family and friends, and all those who have been affected by this tragic event,” the royal added, before signing off the tweet on her shared official account with “C.”
Appearing at the vigil, Nessa’s sister Jebina Yasmin Islam, spoke of the pain of losing her sibling, describing her sister as a “brilliant” woman.
“We have lost an amazing sister far too early … Sabina loved her family. We have lost our sister, my parents lost their daughter and my girls have lost such a brilliant, loving, caring auntie,” Islam said.
“This feels like we’re stuck in a bad dream and we can’t get out of it,” she added.
Residents in Kidbrooke, a quiet London suburb around 20 minutes by train from central London, have been left shocked by the killing in their community.
“You feel it might have happened to you. It might happen anywhere,” Aliya Isaeva, a young mother who has lived in the area for about two years, told CNN on Friday night.
Manuela Colombini, who also attended the vigil and has lived in the area for about 15 years, said: “We want to feel safe. I have two young daughters and I don’t want them to grow up and think that they cannot go out in the streets or to a park,” she said.
CNN’s Vasco Cotovio, Claudia Rebaza, Kara Fox, and Ivana Kottasova contributed to this report.