A statutory tort is like any other, in that it imposes duties on private or public parties, however they are created by the legislature, not the courts. For example, the European Union's Product Liability Directive imposes strict liability for defective products that harm people; such strict liability is not uncommon although not necessarily statutory.
As another example, in England common law liability of a landowner to guests or trespassers was replaced by the Occupiers' Liability Act 1957