A spokesperson for Apple confirmed that while the feature to add a COVID-19 vaccination card specifically to Apple Wallet is not available just yet, it will be in an upcoming update.

This article explains how to add a gift card to your Apple Wallet. Instructions apply to gift cards from payment or banking companies (e.g., Visa, American Express, Mastercard); gift cards from ...

If someone is deep into the Apple ecosystem, an Apple gift card is a great option and you can also add it to your Apple Wallet.