Browder's complaint was originally filed in March and was dismissed a month later as the transfers involving Swedish accounts had occurred before tighter anti-money laundering legislation was introduced in 2014 and as the statute of limitations had expired in the case.
Browder appealed, but the EBM said it had rejected his appeal.
"It is correct that the EBM has decided not to change that decision," a spokesman for the EBM said.
The CEO and chairman of Sweden's oldest bank have both left as money laundering allegations have come under scrutiny from Baltic and U.S. authorities.
Browder, an investor who campaigns to expose corruption, has taken criminal complaints against Swedbank to Swedish, Estonian and Latvian authorities, alleging that accounts at the bank were used to launder $176 million (136.4 million pounds) between 2006 to 2012.
Allegations against Swedbank, mostly reported by Swedish TV, have linked it to a scandal at Danske Bank, which faces potential lawsuits, fines and sanctions after admitting last year that 200 billion euros ($225 billion) of suspicious payments had flowed through its Estonian branch between 2007 and 2015.
(Reporting by Helena Soderpalm; editing by Simon Johnson and Jason Neely)