The arrests were made across the US over the past 10 days after an undercover operation that spanned 10 countries.
The Liberation Tigers of Tamil Eelam (LTTE), which has fought for two decades for an ethnic Tamil homeland, was designated a foreign terrorist organisation by the US in 1997.
The suspects are accused of raising money through "front charitable organisations", money laundering and conspiring to help the group "bribe its way off [the] foreign terrorist organisation list".
Alberto Gonzales, the US attorney-general, said in a statement: "These defendants allegedly sought to obtain, through a variety of means, weapons and materials to carry out a deadly campaign of violence."
An FBI spokesman said that the charities investigated included the Tamil rehabilitation organisation, which transferred large sums of money from London to Sri Lanka, and the world Tamil coordinating committee.
Prosecutors said that being on the foreign terrorist list prevented the group from legally raising money or buying equipment in the US and hampered efforts to appear as a legitimate "liberation" movement.
Analysts say that a 2002 ceasefire reached between the Tigers and the Sri Lankan government appears dead and that a civil war that has already killed 65,000 has resumed.