Upvote:1
This blog post indicates that there are a few companies providing luggage storage. CleanUpAir [what a name...] and SpaOnAir [I think, the Korean version is not that obvious] are on B1, near the train station entrance. Hanjin and CJ are on the check-in counter floor, near M and A respectively.
Upvote:6
Neither the airline nor the airport will store your luggage for you, but there is a left-luggage service at Seoul/Incheon available in both terminals.
You can book storage online at www.trazy.com Prices vary by size and storage period, but a 'medium' item will cost you US$11.20 for two days. Note that each item you want to store is priced separately.
The company also has other sites in Seoul that might suit your itinerary better.
Disclaimer: This is just one possible service I identified on the web. I make no recommendations, and other services may be available.