The 40-year-old Misbah had opted to sit out Pakistan's third one-day international against Australia in Abu Dhabi and all-rounder Afridi was named to lead the side.
Afridi's comments at a news conference gave rise to speculation that he was in line to lead the team during next year's World Cup and hinted at strife within the team.
Khan stepped in to defuse the controversy and reiterated that Misbah would remain in charge through next year's showpiece event in Australia and New Zealand.
"As far as the PCB is concerned, we are supporting Misbah and he is our captain till the World Cup," Khan said. "The remarks made by Afridi are regretful and unfortunate and perhaps gave the indication of something wrong in the team.
"We are looking into Afridi's statement to see whether he has violated his central contract terms and if this is so disciplinary action can be taken against him."
The 34-year-old Afridi, who has played 384 ODIs, said he was ready to lead the team and the board should decide quickly who they wanted as captain in the World Cup.
His remarks fuelled speculation that Misbah, who has been leading Pakistan since 2010, was put under pressure to step aside for the third ODI.
Khan said Afridi should have been more careful with his words and added that Misbah had himself opted to sit out because he was worried with his form.
"I had a long talk with Misbah and he remains our captain but he himself has said that if he doesn't get runs in the coming tests against Australia and New Zealand he doesn't want to be a burden on the team," Khan said.
Afridi later said it had been an honour to captain Pakistan but stressed that it was a very difficult job.
"Trust me, it is no bed of roses, and all of us who have captained Pakistan, including Misbah, are fully aware of it," he said.
"We get nothing more out of it than pride and honour; seldom do we get bouquets but more often brickbats.”
Misbah has been Pakistan's leading run scorer in tests and ODIs over the last three years but has struggled since the tour to Sri Lanka in August.
He also failed to get runs in the first two ODIs against Australia, who swept the three-match series.
(Editing by Sudipto Ganguly and Ed Osmond)
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