Hamilton, who is to leave McLaren for Mercedes at the end of the year, was taking his cue from a tweet by a journalist suggesting Button had unfollowed him on the social networking site.
It led Hamilton to heavily criticise the 2009 world champion.
In a series of tweets on his official feed, Hamilton wrote: "Just noticed @jensonbutton unfollowed, that's a shame. After 3 years as teammates, I thought we respected one another but clearly he doesn't.
"Funny thing is, we are STILL teammates! All good tho, I plan on giving this team & fans all I got til I cross the finish line in Brazil!!!"
But the 27-year-old was left red-faced when he realised Button did not follow his Twitter account in the first place.
That led him to tweet: "My bad, just found out Jenson never followed me. Don't blame him! Need to be on Twitter more!"
Hamilton's latest Twitter faux pas could put further strain on his working relationship with Button going into the final phase of the season.
It comes just weeks after Hamilton posted a picture of the telemetry from his and Button's qualifying laps at the Belgian Grand Prix, which the team quickly told him to remove due to the sensitive nature of the data.
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