Johnson (53) took stress leave early this month. He has been staying at Wakari Hospital since about March 5, The New Zealand Herald is reporting.
The Herald understands a large sum of money, which formed a business deal between a Dunedin businessman and Johnson, has not been repaid. It is understood to be about $150,000.
A misconduct hearing is likely to follow.
Otago Cricket Association chief executive Ross Dykes last night said the nature of the complaint represented a serious breach of trust.
''The association was made aware of an allegation involving Mr Johnson and raised it with him. It has since accepted his resignation,'' Dykes said.
''This has been a very sad and disappointing episode for all concerned.''
Dykes would not comment further on the nature of the misconduct.
''We've . . . said as much as we can and, until such time that things fall into place, there is not a lot more we can say.''
Dykes was ''confident'' Johnson would not face criminal charges. He would not comment on the sums of money involved.
Asked how Johnson was faring, Dykes said: ''It is a delicate subject when it comes to health, but he has to spend a bit of time recuperating and recovering.
''He certainly has some good personal support and he will get the support from Otago cricket in the way we can help.''
Dykes spoke to Johnson yesterday morning and accepted the coach's resignation.
Johnson apologised in a statement for his conduct.
''I have made some very bad decisions around my personal finances which have compounded to a point where I have let down Otago cricket and myself,'' Johnson said.
''I sincerely regret my actions and must now concentrate on restoring my health so I can do my best to make amends.''
Johnson, a seam bowler who took 64 wickets in 27 first-class games for Otago and played 20 one-day games for the province, joined Otago as head coach in June 2011.
He replaced Mike Hesson, who is now New Zealand coach. Last April, Johnson's contract was lengthened by another two years.
This was Johnson's second stint as Otago coach, after first having the role from 1995 to 1997.
Johnson guided Otago to the HRV Cup domestic twenty20 title in 2012-13, and took the Volts to the Champions League tournament in India late last year.
Johnson had previously been Wellington's coach, from 2000 to 2006. He was regarded warmly for his work with the players at that time and at Otago.
Johnson had become a respected bowling coach, and had positions at New Zealand Cricket, including that of a specialist fast bowling coach role from 2007 to 2010.
Johnson's job as Otago head coach has been filled temporarily by Nathan King from early this month. There are four rounds of the 50-over Ford Trophy and finals to round off the domestic season.
New Zealand Cricket did not want to comment on the matter last night.
- Additional reporting Adrian Seconi
