"Oh dear," he tweeted around 11am AEDT on Sunday (1pm NZT).
"I think Australia is waking up again ... time to prepare for another deluge of tweets."
Mr Joyce later tweeted that Qantas had contacted him "with a graceful apology", which could indicate not all his new followers were friendly.
Also making an appearance on Twitter was a fake Alan Joyce, whose account described the tweeter as "leading Qantas Airway to its biggest disaster yet and then on to the next".
The fake Joyce was quickly acquiring followers, up from about 300 on Saturday evening to almost 2000 on Sunday afternoon, as he racked up more than 470 tweets.
Qantas itself was also a major topic on Twitter, with many tweeters expressing their disappointment with the airline's action.
Among them was NSW federal Labor MP Mike Kelly, who tweeted his followers: "Finding it increasingly difficult 2 accept credibility of Alan Joyce. Worried we will see the flying roo give way 2 the flying pig emblem."
- AAP