Trump announced Wednesday a ban for those entering the United States from 26 European countries. The travel restriction is due to start Friday and last for 30 days.
"I am not to judge one measure or the other by any government. But I doubt very much that diseases have passports and are aware of borders," Lagarde told CNBC's Annette Weisbach Thursday.
"They ignore those borders and I think all economies should be mindful about taking the right steps to protect households, the people, enterprises, and make sure, as I said, we bridge that collectively," she added in an exclusive interview.
Her comments come after the ECB decided not to cut interest rates, despite market expectations for a reduction amid the ongoing coronavirus outbreak. However, the central bank did announce measures to support bank lending and expanded its asset purchase program by 120 billion euros ($135.28 billion).
Market participants were expecting a rate cut of 10 basis points as a way to stimulate the euro economy amid fears that a recession is about to hit the region. Both the Federal Reserve and the Bank of England cut rates over the last week as ways to support their respective economies.
Lagarde told CNBC that the ECB was "fully committed to avoid any fragmentation in a difficult moment for the euro area." Her comments were seen as a walk back from an earlier press conference where she said that she was "not here to close spreads" in regards to bond markets. The words caused Italian bond yields to spike.
There are more than 127,000 confirmed cases of the virus worldwide and the outbreak is weighing on all major economies, leading economists and financial institutions to lower their forecasts for global growth in 2020.
In what was Lagarde's first big monetary policy announcement since starting the job in November, she asked euro area governments to present an "ambitious" fiscal package to reduce the economic impact of the pandemic.
"Every crisis is different. The moment we are in is different from 2008. What I certainly tried to impress upon (European) leaders and what the Governing Council of the ECB called for is an ambitious and collective fiscal approach, because when you analyze the crisis at the moment it requires a fiscal approach," Lagarde told CNBC.