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, thats 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 comments can only have left Button unimpressed, and could put a strain on their working relationship at a crucial stage of the season.
The faux pas marked the final chapter of a tough week for Hamilton. His move to Mercedes was the talk of the paddock at the Japanese Grand Prix and he refused to answer questions about it at an FIA press conference on Thursday.
His weekend was scarcely better on the track with a fifth-place finish at Suzuka, as Sebastian Vettel took victory, leaving him still 42 points adrift of points leader Fernando Alonso, despite the Ferrari driver's first-corner accident.
And Hamilton admitted after the race that his title hopes are fading.
He said: "I am quite realistic, I know my situation, but the Red Bulls are going to be hard to beat.
"I got some points but there is not much more I can be happy with.
"The fight is still on with Fernando not finishing so we will keep pushing."
He added: "Everyone should be concerned (by Red Bull's pace), they are very quick, they are always very quick in Korea and Sebastian has scored 50 points in the last two races, Fernando should be more worried than I am.
"I didn't get many points so the championship is not tight for me. I am a long way away, it's going to be very difficult but I will never give up and keep pushing and hopefully we will have a better weekend next weekend."
Hamilton's Twitter climbdown is not the first time he has mis-stepped on the social networking site.
At the Belgian Grand Prix he posted a picture of the telemetry from his and Button's qualifying laps, which the team quickly told him to remove due to the sensitive nature of the data.