Tap the messages icon (it looks like the Facebook Messenger icon). If you see the older default paper airplane icon instead, you will not be able to react to messages with emojis. To fix this, try updating your Instagram Messenger. Go to your profile, tap the three-line menu icon, then tap Settings > Update Messenging > Update. If that doesn’t work, make sure you have a Facebook Messenger account signed in on your phone or tablet. [1] X Research source

Although you can use the website to react to messages, you can only change the default icons from the mobile app. Tap the messages icon (it looks like the Facebook Messenger icon). Tap the conversation to see individual messages.

You’ll see a confirmation message in the text above the emoji menu.

Once you click an emoji, it will be added to the bottom of that message as your reaction.