Combine strawberries, coconut milk, sugar, salt, and vanilla extract in a blender or food processor; process until smooth. Chill mixture for 2 hours in the refrigerator.
Fill popsicle molds with chilled mixture. Freeze for about an hour, then insert popsicle sticks and freeze overnight. To unmold, let popsicles stand at room temperature for 5 minutes. Carefully remove from molds and serve right away, or wrap each one in parchment paper and put back in the freezer for later consumption.
Note: Frozen strawberries can be used in place of fresh strawberries. If using frozen strawberries, skip the chilling step and instead just pour the mixture right into the popsicle molds.