The men were detained on suspicion of facilitating illegal immigration and entering the UK illegally.
Five people, including a seven-year-old girl, were killed in a crash onboard a boat crossing the Channel.
The boat was carrying 112 people at the time of the tragedy.
Police identified the men as two Sudanese nationals – aged 22 and 19 – and a South Sudanese citizen, also aged 22.
The statement, issued by officials on Wednesday lunchtime, said the men were arrested in a Tuesday night raid by NCA and Immigration Enforcement officers.
Officers have already conducted initial interviews with the men, and with further interrogations to follow in the coming days.
The three are being questioned by officers at a police station in Kent.
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