BRUSSELS—The European Union’s executive arm said it was opening a probe into Illumina Inc.’s decision to complete its $7.1 billion purchase of Grail Inc. despite a continuing antitrust investigation.

The European Commission said Friday that the probe would assess whether Illumina’s move breached the bloc’s rules calling for companies to put on hold mergers while the EU is investigating competition concerns.

“We deeply regret Illumina’s decision to complete its acquisition of Grail, while our investigation…is still ongoing,” said European Commission Vice President Margrethe Vestager, who leads the EU executive’s antitrust work. The commission takes “very seriously” breaches of companies’ standstill obligation, she added.

If the commission decides Illumina has breached its rules, the company could be fined up to 10% of its revenue.

San Diego-based Illumina develops and sells next-generation genetic-sequencing machines and the chemicals used in them. Grail, based in Menlo Park, Calif., was founded by Illumina and spun off in 2017. It has been developing liquid biopsy tests that examine blood samples for genetic signs of cancer—a product that, if successful, could have a significant impact in healthcare. Illumina has said buying back Grail would allow it to scale up operations and more quickly expand access to the tests.