Most places say you need to be 21+. Lets have a look at the terms and conditions of the biggest online suppliers of nicotine pouches:
Zyn.com: “To place an order, you may either need to provide evidence of your age or confirm that you are above 18” (source)
Nicokick.com: “People under the age of 21 are not permitted to place orders” (source)
Northerner.com: “People under the age of 21 are not permitted to place orders” (source)
BNBtobacco.com: “You must be 21 years or older to buy our products in accordance with current FDA regulations” (says it on every page)
Note that the Tobacco 21 legislation (requiring anyone purchasing any tobacco product to be 21 and older) couldn’t apply to nicotine pouches, since they contain no tobacco. I wasn’t able to find a definitive source for any kind of legislation pertaining to nicotine pouches specifically. However, my guess would be that you should be 21 to purchase nicotine pouches.