John Woodcock called moves by McDonnell to abolish the compliance unit that checks party membership applications to weed out unsavoury characters "sickeningly irresponsible".
He claimed the move would damage party officials' ability to kick out disreputable members, citing paedophile Tom O'Carroll's recent ousting as evidence of its value.
Woodcock, who backed Liz Kendall at the Labour leadership contest, also blasted the Hayes and Harlington MP for attaining high office without election, saying the frontbencher cared more about turning Labour into "the play thing of his dodgy mates".
In a string of tweets, Woodcock said McDonnell being given one of the most important jobs in politics to hold the Government to account.
But he claimed that the shadow chancellor cared more about appeasing far-left activists, whom the unit might deny membership.
He finished by saying moves to abolish the compliance unit would "give paedophiles, terrorists anti-Semites and anyone else a free run to join up and tarnish our party", asking: "Is that what he wants?"
According to the original Times report, McDonnell told a meeting of the 'Momentum' group that he was lobbying the national executive committee to alter rules that mean those deemed to "not support the aims of values" of Labour could be thrown out.
People had already been expelled for “spurious reasons”, he said.
The Huffington Post UK contacted McDonnell for comment but his office did not reply by the time this story went live.