Officers are hunting a second attacker who also tried to target a branch of the Kabul Bank in Khost city.
"A suicide bomber was killed by police before entering Kabul Bank in Khost. He did not detonate. One guard was wounded in the incident," the interior ministry said in a statement.
"A suicide bomber was shot dead by police before reaching his target in front of the Kabul Bank branch in Khost city," Khost provincial police spokesman Zirat Gul Mangal said.
"A second bomber is at large in the city and a massive operation is under way to hunt him down."
Khost, which borders Pakistan, is a stronghold of the Haqqani network, a faction of the Afghan Taliban loyal to al Qaeda and blamed by the Americans for some of the most-high profile attacks in Afghanistan.
In February, a gun and suicide attack on a branch of the Kabul Bank left 38 people dead in Jalalabad, which is also near the Pakistani border.
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Well done Afghan Police. The suicide bomber might have caused a massacre if were allowed to carry out their terrorist act.