Whisk the oat milk, coconut milk, granulated sugar, cornstarch, orange zest, and salt together in a saucepan until no lumps remain.
Cook over medium heat, whisking constantly, until the mixture bubbles and thickens into a light pudding. Continue cooking for 1 minute.
Remove the pudding from the heat and whisk in the orange juice concentrate and vanilla extract. Let it cool for 15 minutes, stirring occasionally to prevent a skin from forming.
Divide the orange pudding among eight popsicle molds and insert the sticks. Freeze for at least 6 hours until completely solid.
Hold each mold under lukewarm water for several seconds, then gently release the pudding pops and serve immediately.
