Iceland is a signatory to the Schengen Treaty.
Between nations that have signed and implemented the pact, there are usually no border restrictions. This covers the majority of the European Union as well as a few additional nations.
Before boarding foreign planes or vessels, identification checks are typically performed. At land boundaries, there are sometimes temporary border restrictions.
A visa issued to a Schengen member is also valid in all other Schengen nations that have signed and implemented the treaty.