The attack occurred around 3 PM local time (1300 GMT) before shoppers apprehended the knifeman, identified only as Konrad K, and handed him over to police.
"The man acted irrationally, stabbing people in the back. One of the wounded women died. Seven other people are injured," police said in a statement.
Officers said the man had no criminal record and was sober. He is being tested for drugs.
"The police are trying to establish the circumstances of the incident and above all, the reasons behind it," government spokesman Rafal Bochenek told the Polish PAP press agency.