The blast came hours after a similar bombing killed three people elsewhere in the region.
Footage on the CNN Turk channel showed offices inside the police station in ruins and filled with smoke after the bomb exploded just outside the complex at 9.20am local time, when police had already begun arriving for work.
No one immediately claimed responsibility, but Defence Minister Fikri Isik told the state-run Anadolu Agency that the Kurdistan Workers' Party (PKK), deemed a terrorist organisation by Turkey, the United States and the European Union, was behind the attack.
"The people see the real face of the PKK," Isik said.
The PKK has carried out dozens of attacks on police and military posts in the largely Kurdish southeast since 2015.
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Five police killed in PKK attack in eastern Turkey: official
But Elazig, a conservative province that votes in large numbers for the ruling AK Party, had been spared violence until now.
Video footage showed a plume of black smoke rising above the city after the blast, which uprooted trees and gouged a large crater outside the police complex, located on a busy thoroughfare in the city of 420,000 people.
In Van province, further east, two police officers and one civilian were killed and 73 people were wounded late on Wednesday when a car bomb exploded near a police station, the local governor's office said in a statement.
There were also no claims for the attack in Van, a largely Kurdish province on the Iranian border. The Van governor's office said the PKK was responsible.
The southeast has been scorched by violence since a 2-1/2-year ceasefire with the PKK collapsed in July last year.
Thousands of militants and hundreds of soldiers and police officers have been killed, according to official figures. Rights groups say about 400 civilians have also been killed.
The PKK wants greater autonomy for Turkey's 15 million Kurds.
More than 40,000 people have been killed in violence since it first took up arms in 1984.
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