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Douglas Chapman, the MP for Dunfermline and West Fife, announced he had resigned as national treasurer of the party on Saturday evening.
Mr Chapman took over in the role last year.
On Twitter, he said: "Despite having a resounding mandate from members to introduce more transparency into the party's finances, I have not received the support or financial information to carry out the fiduciary duties of National Treasurer.
"Regretfully I have resigned with immediate effect."
It is not clear what led to Mr Chapman's decision, but SNP business convener and fellow MP Kirsten Oswald said she "fundamentally disagrees" with Mr Chapman's assessment.
Also on Twitter, she said: "I am disappointed by Douglas' decision and, as business convener, fundamentally disagree with his assessment of the support and financial information available to him.
"However, I respect his decision, thank him for his contribution to the NEC (National Executive Committee) and wish him well.
"SNP national treasurers have access to detailed financial information and report to the NEC on a monthly basis.
The NEC can request any additional information it requires.
"The SNP's accounts are also independently audited, submitted to the Electoral Commission and published."