Adero Law said it filed the class action on Friday for more than 7,000 current and former employees of Woolworths Supermarkets over the scandal, which has drawn criticism from opposition politicians and prompted an investigation by a government agency.
In October, Woolworths said it had underpaid thousands of supermarket workers for years and would need to repay as much as A$300 million, becoming the highest-profile company to be caught up in wage scandals across corporate Australia.
Adero Law said it "considers that the underpayments disclosed by Woolworths to date substantially understate the wages owed," and put the number much higher at A$620 million.
Woolworths intends to defend itself in the proceedings, and said it hopes to make interim payments to affected current and former staff before Christmas.
"Woolworths Group believes the class action proceedings are without merit," the company said in a statement.
Woolworths shares touched a record high of A$40.04 earlier in the session, and were up 0.1% at A$39.805 by 0407 GMT.
Other cases of staff underpayments in recent years have included retail conglomerate Wesfarmers, Super Retail Group, and jeweller Michael Hill International Ltd among others.
Last week, Woolworth's Chief Executive Officer Brad Banducci said he would forgo his bonus following the scandal, while Chairman Gordon Cairns would take a 20% cut to his board fee.
Government agency the Fair Work Ombudsman is investigating the underpayments by Woolworths.
($1 = 1.4736 Australian dollars)
(Reporting by Niyati Shetty and Nikhil Kurian Nainan in Bengaluru; Editing by Lincoln Feast.)