Parts of the city were in lockdown following the incident with one suspect in custody and a manhunt underway for an accomplice still at large, the interior ministry said in a statement.
The detained man is accused of killing a local resident during a carjacking and attacking a police station at around 11 am (local time), shooting a police officer and taking his gun, said the statement.
The suspect then shot two officers as they gave chase before being arrested.
It said that police are now searching for the gunman's "partner in crime."
Local media reported that at least seven police are being treated in hospital.
The country's anti-terror service has issued a red alert threat warning following the attacks and police have called on residents of the city to stay in their homes.
A woman who lives in the Almalinsky district of Almaty where the police station was attacked told AFP the situation in the city was "very tense".
Several areas of the city have been cordoned off including the city's railway station, witnesses told AFP.
The country has been rocked by several violent incidents in recent months.
Gunmen went on a rampage in the northwestern city of Aktobe near the Russian border on June 5, killing three civilians at two gun stores before trying to storm a military base with a hijacked bus, killing three soldiers.
In a statement on last month's violence President Nursultan Nazarbayev called the attackers "followers of radical pseudo-religious groups" adding that the gunmen had operated on "instructions received from abroad."
For much of its independence Kazakhstan was able to avoid the kind of political tumult seen in other countries in ex-Soviet Central Asia.
But growing social dissatisfaction in the majority Muslim nation has grown as the economy reels from low oil prices and a crisis in neighbouring Russia, a strategic ally.
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