One euro was worth $1.0987 at 1915 GMT, down 1.20 percent from Friday night, in electronic trading before Asian markets opened.
Earlier in the day, the euro had fallen to 1.0963 dollar, with about 50 percent of votes counted in the Greek bailout vote.
The early official results showed that more than 61 percent of Greeks had voted 'No' to creditor demands for further austerity in return for a bailout.
A failure to reach a deal with the creditors could trigger a Greek exit from the eurozone, and after the ballot, Greece's government said it would step up efforts to reach a bailout agreement with creditors.