The decision comes only a week after Iran won its tenth AFC Futsal Championship title after beating Uzbekistan in the final match.
Shams said he decided to resign as he could no longer work with the Iranian football federation under the current conditions, Mehr News Agency reported.
Shams was quoted as saying by Mehr that the Football Federation of the Islamic Republic of Iran (FFIRI) was not committed to the financial terms of his contract and said he had not been paid for five months.
His resignation has been accepted by FFIRI head Ali Kafashian, Mehr said.
Shams has been the Iranian national Futsal team's manager in two terms. His first term began in 1999 and ended one year later.
After Iran ended as runner-up in the 2006 Asian Championship, Shams returned to the national team, leading Iran to the second round of the Futsal World Cup in 2008 and three successive Asian titles in 2007, 2008 and 2010.
Since the beginning of the Asian Futsal Championship in 1999, Iran has claimed 10 of the 11 titles, losing the 2006 tournament to Japan.