The teenager is accused of stabbing 69-year-old Susan Addis to death at her home in Cedar Gardens, Withdean.
Ms Addis, who ran Donatello's Italian restaurant, was found dead at the house at around 7pm on Thursday.
Her family said in a statement issued through police: "At this very sad and distressing time, the family kindly asks that all media respect their privacy. The family are currently in a state of shock".
Brighton MP Caroline Lucas described Ms Addis as a "special presence" as she paid tribute to the grandmother's fundraising efforts in the town.
"So shocked and saddened to hear devastating news of death of the amazing Sue Addis," she tweeted.
"So many in Brighton will be heartbroken - she was such a special presence in the city, her passion for this place & its people was infectious, and her kindness legendary. She'll be hugely missed".
Hove MP Peter Kyle said: "Desperately sad news. There was barely a positive event, campaign, or good cause without Sue being part of making it happen... Our city misses her already."
Sussex Police said that Ms Addis and the suspect were known to each other.
"Police are not currently looking for anyone else in relation to the crime and there continues to be no risk to the local community," the force added in a statement.
"The investigation is being carried out by detectives from the Surrey and Sussex Major Crime Team, working with local officers."
The teenager was charged with murder on Friday night and was due to appear at Brighton Magistrates Court on Saturday.