Deputy Police Commissioner, Seelall Persaud said the man was arrested at the Springlands back track, Corentyne River.
He has been identified as Jermaine Maynard of Leopold and Cross Streets, Werk-en-Rust, Georgetown.
Investigators said Maynard shot 20-year old Matthews to her head outside KFC Stabroek Market about 11:45 Tuesday night.
Matthews, the mother of a five year old boy, was standing with her mother when Maynard allegedly called her on her phone to go across the road. There, he allegedly lit two loud squibs before he shot her and escaped.
In October last year, Matthews was charged with causing Maynard grievous bodily harm but the case was dismissed after he declined to give evidence against her.