The 24-year-old man is being questioned on suspicion of criminal damage after he was stopped with chainsaws in his car.
Between 50 and 60 trees, some of then more than 20ft high, were felled.
Furious residents reported the damage to the police and officials from Elmbridge Borough Council who have been hunting for the culprit.
Officers detained a man on Thursday in connection with the incident.
A statement from Surrey Police said: “Residents contacted us with information, allowing investigating officers to identify a vehicle they believed to be connected.
“Last night, this vehicle was stopped. Searches carried out in the suspect’s car and home address found several chainsaws and wood chippings. The man was arrested and remains in custody.”
Locals had been patrolling the riverbank themselves in the search for the man who operated in the dead of night to avoid detection.
Police trawled through CCTV footage but drew a blank until the arrest this week.
Anthony Cilia, a retired kitchen fitter from Weybridge, was among the first to spot the damage to the trees.
He told MailOnline: “Why this person is doing it is beyond me. There are plenty of wooded areas nearby to go to, but for some reason they are choosing to do it in a public area on the banks of the river.
“Not only is it a blight on an area the council has spent several millions of pounds on improving, but more importantly, it’s dangerous.”
Another local resident, Christine Elmer, said some of the felled trees had been grown especially in memory of loved ones who had died.
She tweeted: “Really important if anyone has any info on who is going around our town and wider borough cutting down trees, including memorial trees, to get in touch with the Elmbridge Police.”
Inspector Bert Dean, the borough commander for Elmbridge, said: “This is an encouraging development in this investigation. We continue to piece together the evidence we have. Thank you again to the local community for their ongoing patience and support.”