The agency wants to keep large asset managers from swaying banks where they have big stakes.
The Federal Reserve said that its penalty was for Citi violating an enforcement action from 2020.
The move follows about $3 billion in fines imposed on financial firms over private messaging.
Barr also repeated his long-standing view that the US banking sector is sound with “no signs of liquidity problems.”
Nevertheless, the overall banking system "remains sound," the central bank said.
The Fed wants to know about the wealth management arm's measures to prevent money laundering.
The too-big-to-fail tag spells greater oversight and fresh compliance headaches.
Backers say the measures will help rein in claims about ESG investments.
Banks say reforms after the 2008 financial crisis give an unfair advantage to less-regulated nonbank lenders.
U.S. regulators are weighing the prospect of downgrading private assessments of the bank.
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