Air carrier Captain reported receiving an airborne notification of undeclared Hazmat cargo onboard. Hazmat was determined to not pose a safety of flight concern and flight continued to destination.

Narrative

About 10 minutes after departing ZZZ bound for ZZZ1 dispatch sent a massage via ACARS to the flight deck stating they had just been informed by ground ops we were Carrying 3lbs of corrosive Hazardous Material and asked if we were aware of it. After we responded we didn't know; the load and the category of the load had not been disclosed in any way to the flight crew; Dispatch recommended we returned to the field. ZZZ had just experienced a runway flow change and winds were deteriorating; we decided It was not the best airport to divert to. At this point we were south of ZZZ2 almost abeam ZZZ3 and ZZZ4. Captain suggested we could go to ZZZ3 if needed and we asked dispatch if they know this was a safety of flight concern and dispatch responded back to standby while they reached a supervisor. A few minutes later they said to divert to ZZZ5We started the diversion and about 10 minutes later they said to continue to ZZZ1 ( original Destination) after they determined it was not a Safety of Flight problem. We landed in ZZZ a some time later with no further incident. After landing a supervisor came up to the flight deck and requested the flight deck copy of the report.Cause: Miss communication between ground operations and flight crew. Loading Hazardous Material in the cargo bay and not disclosing it in the report and or to the flight crew.Suggestions: Having a Ramp supervisor issue an alert to the person doing the report about the Hazardous Material to be carried onboard. Modifying the report to ask and certify there is no presence of cargo that must be disclosed and handled differently due to its nature.