Police responded to the campus on the 6200 block of Keystone Street Wednesday morning.
Students were released and others were turned away when they arrived around 8 a.m., police say.
Police are investigating the posting that included the picture of a high-powered gun as an implied threat.
There has been a rash of recent fights involving a number of pupils at the 9th through 12th grade school of 400 students.
"I heard it was a threat of guns or a picture of a gun, and then there have been some fights. But I want to stress Tacony (Academy Charter) is an excellent school," parent April Sudler said.
Top school officials say the shutdown was the prudent thing to do.
"We just received information from one of our parents that there was a possible threat on social media and because we didn't have enough information to know that if it was credible or not, we decided to investigate with law enforcement so we can ensure safety," said Ashley Redfeam, CEO of Tacony Academy Charter.
Social media threat to local charter school featured pictures of guns..school shut down as cops investigate pic.twitter.com/TgCny8YhH6— Vernon_Odom (@Vernon_Odom) March 2, 2016
"We're still investigating the reasons behind the off-campus assaults and all students will be treated fairly and we will follow our code of conduct when issuing consequences, if necessary," school principal Naimah Holliday said.