The arrest comes a day after the incident at a Tesco Express store in Goring Way, at about 7.50am, on Saturday (October 21).
"A man walked into the store, threatened the staff at knifepoint and demanded cash from the till,” a police spokesperson said.
"He made off with £150. No was harmed.”
An urgent manhunt was launched by Sussex Police on Saturday.
In an update on Sunday, a statement from the force read: “Detectives investigating an armed robbery at a Tesco Express store in Goring have arrested a man.
“A 20-year-old local man was arrested on Sunday on suspicion of committing robbery and is currently in custody.”
Police said the investigation is ongoing and officers are ‘continuing to appeal for witnesses to the incident’, adding: “If you can help our investigation, report online or ring 101 quoting serial 265 of 21/10.”