The request for information is the first step in a process begun under the EU's Digital Services Act (DSA), but does not itself indicate there have been legal violations or a move towards punishment.
The European Commission said it wanted "more information on how" Apple and Google "have diligently identified any systemic risks concerning the App Store and Google Play".
It also wants the companies to demonstrate that they have complied with rules on digital marketplaces and transparency about adverts in order to protect users online.
Apple and Google must respond by January 15.
The DSA is one of the EU's mammoth new laws to bring big tech to heel, with stricter rules on policing content online and ensuring that digital consumers have a safer experience.
The commission has already launched a slew of other probes against big online platforms, such as Amazon, seeking information about how they are complying with the DSA.
If a platform violates the DSA, it risks a fine of up to six percent of global turnover.
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