The landmark law, which comes into effect in 2023, imposes strict competition rules on Meta and six other companies seen as gatekeepers to the internet.
Sources said the fine is expected to be in the hundreds of millions of dollars and could even exceed $1 billion.
Industry insiders added that the EU's investigation into the parent company of Facebook and Instagram is expected to end as early as this week, and the Commission will immediately announce enforcement actions.
EU officials are also expected to issue a "cease and desist" notice to Meta, telling the company what changes it must make to comply with the rules, according to sources.
Representatives for Meta and the European Commission did not immediately respond to requests for comment.
Apple has also become a thorn in the EU's side, with fines against the iPhone maker likely to be announced this week or next, sources said.
Earlier this month, Reuters reported that Apple and Meta could face "modest fines" for violating the DMA. EU antitrust chief Theresa Ribera previously said that enforcement actions against the two companies will be decided in March.
In addition to Meta, companies considered "gatekeepers" under the DMA include Google parent Alphabet, Amazon, Apple, Booking.com, TikTok parent ByteDance and Microsoft. EU regulators and other backers say the law prevents tech giants from suppressing smaller rivals through anti-competitive behavior.
Under the law, large tech companies can be fined up to 10% of their global revenue. Repeat violations can result in fines of up to 20% of global revenue.
In July last year, the EU filed preliminary charges against Meta, accusing it of violating the DMA by forcing customers to adopt a restrictive "pay or consent" model for advertising on Instagram and Facebook.
Officials focused on a subscription service Meta will launch in 2023 that would allow users to pay the equivalent of $14 per month for an ad-free app experience or consent to Meta using their personal data to serve targeted ads.
"This binary choice forces users to consent to the aggregation of their personal data and fails to provide them with a less personalized but equivalent version of the Meta social network," the European Commission said in a statement at the time.
In a public compliance report released earlier this month, Meta complained that despite efforts to comply with DMA rules, it "continues to receive additional requests that go beyond what is legally required."
In June 2024, Apple became the first company to be accused of violating the DMA for allegedly preventing rival app developers from easily directing customers to services outside its App Store. In November, there were reports that Apple could be fined.
The European Union took further action last week, warning Apple that it must open its iPhone operating system to app developers. The EU also told Google parent Alphabet that it could face fines if it gives "more preferential treatment" to its own internal services in search results.
In addition to drawing sharp criticism from Big Tech, the bill has increasingly drawn the ire of Trump, who has accused Europe of cheating the United States and vowed to impose retaliatory tariffs to level the playing field.
Trump issued a memo last month warning that his administration would "consider response measures, including tariffs, to combat digital services taxes (DST), fines, practices and policies imposed by foreign governments on U.S. companies."
"President Trump will not allow foreign governments to appropriate the U.S. tax base for personal gain," the White House said at the time.
Separately, House Judiciary Committee Chairman Jim Jordan asked EU officials to introduce how the EU plans to implement the Digital Markets Act. Jordan pointed out that six of the seven "gatekeepers" subject to the bill are American companies.
"These severe fines appear to serve two purposes: to force global businesses to comply with European standards and to serve as a European tax on U.S. companies," Jordan said in a letter.
Zuckerberg, who has had a good relationship with Trump since his victory, said the EU fines targeting big tech companies were "almost like a tariff" and "sort of an EU-wide policy against U.S. tech companies."
In January, Zuckerberg said during an appearance on the "The Joe Rogan Experience" podcast that Trump should fight back against fines.
"I think it's a strategic advantage for the United States to have many of the most powerful companies in the world, and I think that should be part of the strategy for the United States to defend that advantage going forward," Zuckerberg said.
The EU and Meta have long been at loggerheads over data privacy issues, including a record $1.3 billion fine in 2023 for improperly transferring European user data to the United States.