Police were called to Friary Way, by the Metro Bus offices, at about midday following the threat and the area was cordoned off.
The area was deemed safe.
A man has now been arrested on suspicion of a bomb hoax and is currently in custody.
Sussex Police said in a statement: "About 12.18pm on Saturday 7 May, police received a report of a bomb threat in the vicinity of Friary Way, Crawley.
"Officers responded and identified the informant, and concluded the scene was safe.
"The man has been arrested on suspicion of a bomb hoax and is currently in police custody."