Several people were injured after police inside fired on the protesters, who then broke into the building’s lower floors and clashed with police.
The abolition of the force has been a demand of protesters who ousted Hosni Mubarak as president in February.
Earlier, new PM Essam Sharaf vowed to meet protesters’ demands for change.
Mr Sharaf was named as head of the transitional caretaker government by the army on Thursday.
He replaced Ahmed Shafiq, who was appointed in the dying days of Mr Mubarak’s rule.
The clashes in Alexandria came to an end when soldiers arrived and took control of the state security building.
Witnesses said officers inside had been trying to destroy papers.
The force is widely accused in Egypt of human rights abuses, including torture of detainees.
One of the demands of the protesters who overthrew Mr Mubarak was an end to Egypt’s decades-long state of emergency.
The military council, which has been running the country since Mr Mubarak stepped down on 11 February, has ordered the government to run the country’s affairs for six months “or until the end of parliamentary and presidential elections”.
They have also promised to end the state of emergency before the elections.
On Friday, it was announced that a referendum on constitutional reform in the country would be held on 19 March.
‘Serve the citizens’
Speaking to an estimated 10,000 people in Cairo’s Tahrir Square, Mr Sharaf said: “I will do my utmost to realise your demands”.
The square was at the centre of protests that toppled Hosni Mubarak.
“I pray that Egypt will be a free country and that its security apparatus will serve the citizens,” Mr Sharaf said after chants broke out calling for the state security force to be abolished.
The protesters had planned Friday’s rally to call for the resignation of Mr Shafiq but went ahead with the gathering as a celebration of the appointment of Mr Sharaf.
A US-educated civil engineer, Mr Sharaf opposed Mr Mubarak’s government after stepping down from the cabinet five years ago.
He actively supported the revolution, joining the street protests in the capital.