Best answer
Yes. A story mention is an inbound event on Instagram, so an automation can trigger on it and reply in the DM thread the mention created. Story replies work the same way.
This is one of the highest intent triggers available, and it is underused. Someone who tags you in their story is showing you to their followers voluntarily. An automated thank you that arrives in seconds, rather than whenever someone checks the inbox, is the difference between a moment and a missed one.
Two things to design around.
Keep it human and short. A story mention is a social gesture, not a support request. A long scripted reply reads worse than no reply. One sentence that acknowledges it, and at most one thing to tap.
The 24 hour window starts at their mention. If your flow waits before replying, it is spending that window.
You can put a keyword filter on the trigger, but for story mentions most people should not: the mention itself is the signal and there is often no text to match against. Leave the keyword list empty and the trigger fires on every mention.
If you also want to reward the mention, this pairs well with a tag: tag the contact on story mention, then treat that tag as an audience later.