The firm is being probed for an accounting cover-up after it admitted to hiding $1.7bn (£1bn) in losses over two decades.
Mr Kikukawa resigned in October after the scandal broke out.
Olympus has sued 19 former and current executives over the issue.
Former executive vice president Hisashi Mori and former auditor Hideo Yamada are the other two people who were arrested.
"This is the first solid increment, taking a system that has governed itself on informal rules, to the one that is based on formal rules and law," Kenneth Cukier7 of The Economist told the BBC.
The scandal broke out in October after former chief executive Michael Woodford claimed he was fired for raising concern about the company's accounting practices.
Mr Woodford pointed out that he had questioned Olympus' payment of $687m in fees to financial advisers during the acquisition of UK medical equipment company Gyrus.
Although the company initially denied the allegations, it later admitted that it had been hiding losses for as long as 20 years.
The scandal resulted in the company's shares plunging more than 50% on the Tokyo Stock Exchange (TSE).
The TSE had also placed the stock under a watch list as the firm delayed filing its latest accounts in the wake of the scandal.
Analysts said the latest developments were a victory for the firm's shareholders.
"It is game over for Kikukawa and other people who have frauded the company and its shareholders of billions of dollars," said Mr Cukier.
"This is a day that anyone who believes in the rule of law should be celebrating."
lympus has been going through a tough time since the scandal broke, not least because of the way in which it has handled the affair.
While it has sued 19 people involved in the cover-up, some of those accused continue to be a part of the firm's management.
Analysts said this was preventing necessary changes from being made at the firm.
"In the case of Olympus, we have a very strange situation," Gerhard Fasol of Eurotechnology Japan told the BBC.
"There is a management in place that is being sued by its own company and has publicly declared that it is not going to take any big decision," he said.
The firm has said that all board members subject to the lawsuit will resign by March or April.
It has also called an emergency shareholder meeting to elect new management.
However, analysts said these steps should have been taken much earlier and that the delay has hurt Olympus.
From bbc news