The international arbitration claim on behalf of the Doha-based channel is being lodged under the jurisdiction of the International Centre for Settlement of Investment Disputes in Washington.
"Al-Jazeera formally initiates arbitration case against the Arab Republic of Egypt," read a statement from the company's London-based lawyers, Carter-Ruck.
Thousands of activists, as well as several journalists, have been detained since then army chief and now President Abdel Fattah al-Sisi overthrew his Islamist predecessor, Mohamed Morsi, in 2013.
The statement said Egypt was in breach of international law as well as a Qatar-Egypt investment treaty intended to protect business interests.
"A large number of journalists working for Al-Jazeera were subjected to harassment, arrest and detention, either without charge or on clearly spurious and politically motivated charges," the statement said.
"Al-Jazeera's facilities in Egypt suffered attacks by the military, police and gangs supporting the military government," it said.
"Al-Jazeera's licence to broadcast in Egypt was also cancelled and its local branch subjected to a compulsory liquidation procedure."
"Al-Jazeera's very significant investment in Egypt has been confiscated and, at a conservative estimate, it has suffered losses of at least $150 million (138 million euros)", it said.
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The ousting of Morsi unleashed a bloody crackdown on protesters that killed hundreds of demonstrators, while militants launched an insurgency that killed hundreds of policemen and soldiers.
Three reporters with Al-Jazeera were detained in 2013 and later convicted of fabricating "false" news in support of the Brotherhood.
Their trial sparked international criticism led by the White House and the United Nations.
One of the Al-Jazeera journalists, Australian Peter Greste, was deported and the other two, Canadian Mohamed Fahmy and Egyptian Baher Mohamed, were eventually pardoned and released.
"Al-Jazeera has now been left with no option but to formally commence legal action," a company spokesman was quoted as saying in Wednesday's statement.
"Al-Jazeers has launched this claim to protect the rights of its staff... together with its own rights under international law," the spokesman said.
Al-Jazeera served Egypt with a formal notice under the Qatar-Egypt investment treaty in April 2014 and Carter-Ruck said that the Egyptian government did not "show any interest at all" in legal discussions.
Sisi, the former army chief who was elected president in 2014, remains popular with many Egyptians as he seeks to put an end to unrest following the 2011 revolution that toppled longtime president Hosni Mubarak.
He has vowed to steer clear of court cases out of respect for the judiciary's independence.