Army bomb disposal experts were called to a flat at Westgate End near the city centre last night and police cordoned off an area of Westgate while the property was examined.
In a statement issued this morning, The North East Counter Terrorist Unit (CTU) said: "We can confirm that potentially suspicious material has been found at the property and examinations are ongoing.
"As a result of the discovery of the material, nearby properties were evacuated and roads were closed as a precaution in the interests of public safety."
Road closures have now been lifted in the area but a safety cordon remains in place as the CTU, supported by West Yorkshire Police, continue enquiries.
The statement said: "Whilst the search continues, public safety remains the priority of investigating officers.
"At this time, this is being treated as an isolated incident.
"Residents will be kept as informed as possible and we are grateful for their understanding, patience and support while the search is concluded."
The address was searched after a 41-year-old man was arrested on suspicion of drugs offences in Leeds on Sunday afternoon.
Officers then searched the man’s home address in Westgate End, Wakefield, at around 4.30pm.
An army bomb disposal team from Catterick arrived at the scene just before 9.30pm on Sunday.
And the team were back at the site this morning.
The man remains in police custody.