The petrol bomb was thrown from the Bogside towards Alexander House on Bishop Street on Sunday night.
The Lecky Road flyover was also blocked with burning bins.
A total of 34 petrol bombs were thrown at police on Saturday night in what was a second weekend of trouble in the area.
Most of the trouble happened at the Fountain estate interface and Nailor’s Row in the city’s Bogside.
Some of the people throwing petrol bombs were as young as 10, according to the PSNI.
Alexander House supports elderly and vulnerable people.
“There are people living in fear,” said PSNI Chief Inspector Alan Hutton.
“There were no injuries but the fear alone is significant. We have to consider the feelings of those vulnerable people in Alexander House.
“Thankfully officers were on hand to put the flames out.
“We have not made any arrests following trouble at the weekend yet. We do have a lot of people traumatised and living in fear following recent events.”
There has been widespread condemnation from the DUP, Sinn Fein, the SDLP and the UUP.SDLP Foyle MLA Mark H Durkan has called for cool heads and leadership after another weekend of violence.
“We welcome more cross community work and it’s great to see the widespread condemnation,” Inspector Hutton added.
“I haven’t heard too much from independent politicians recently though.
“We have stepped up our patrols in the area but there are clearly people being sucked in to cause trouble. It may even be orchestrated.”Tags: