In an interview with CNN's Piers Morgan, Zimmerman said it would be a long time before George's life returned to normal.
"He is still processing the reality or notion of being a free man, of having what the judge described as no further business before the court," Zimmerman said of his brother's post-trial mental state.
In multiple interviews on Sunday, Zimmerman also said that George and his family will always feel threatened by certain "groups" who might seek out "vigilante" justice in Martin's name.
"There are factions, there are groups, there are people that would want to take the law into their own hands as they perceive it, or be vigilante's in some sense," he told Morgan.
"They think that justice was not served, they won't respect the verdict no matter how it was reached and they will always present a threat to George and his family."
Zimmerman echoed the sentiment in a conversation with NPR's Rachel Martin.
"It's a reality that some people don't respect this verdict and think that they want to take justice into their own hands."
He blamed the media for perpetuating the idea that racist thinking motivated his brother to shoot Martin.
"NBC had a lot to do with pushing that narrative by editing George's non-emergency call to the police to suggest ... that George had called the police to report a person who was suspicious because he's black, because he's wearing a hoodie," he said.
Robert's foray into public relations hasn't always been smooth. The 32-year-old was widely criticized for comparing the late Martin to another black teenager who was accused of shooting a one-year-old baby during a robbery back in March.
In a tweet, he wondered whether the robbery incident was an example of why people think “blacks mightB risky."