There are currently queues all the way around the block, from Patrick Street to Oliver Plunkett Street, up Cook Street and back to Patrick Street.
The store was supposed to reopen at 10.30am but eager shoppers were allowed in just after 9am.
The retailers' stores in Cork have been closed since March due to Covid-19 restrictions imposed by the Government.
A spokesperson for Penneys said:
"Employee and customer safety are the highest priority in our preparations for re-opening.
"We are closely following all government safety advice and applying experience gained from our store openings across Europe, putting rigorous health and safety measures in place in all stores, including a strict social distancing protocol, personal protection for employees and customers and increased in-store cleaning."
Primark CEO, Paul Marchant, said:
“We are also asking customers to respect the measures we have put in place to help ensure shopping at Penneys is an enjoyable, safe experience for everyone.”