The benchmark S&P/ASX 200 slipped 0.34 percent, or 14.5 points, to 4,225.1 while the broader All Ordinaries index was 0.36 percent lower, losing 15.4 points to 4,287.6, with analysts saying all eyes remained on Greece.
"We were expecting a relatively soft start to the week amid disappointment after Greece's creditors struggled to reach an agreement on a debt-swap deal," said IG Markets' Stan Shamu.
"A lack of an agreement by now is further unsettling investors and risk assets could come undone should more delays materialise,"
Trade was expected to remain muted during the week-long Lunar New Year celebrations, he added, while Sydney will also close on Thursday for the annual Australia Day holiday.
In New Zealand, the NZX50 index was up 18.56 points or 0.57 percent at 3,295.02.
Financial markets in Hong Kong, Jakarta, Kuala Lumpur, Manila, Seoul, Shanghai, Singapore and Taipei were closed.
The Australian dollar fetched 104.92 US cents, up from 104.00 late Friday.