Special counsel Robert Mueller’s team in mid-October issued a subpoena to President Donald Trump’s campaign requesting Russia-related documents from more than a dozen top officials, according to a person familiar with the matter.

The subpoena, which requested documents and emails from the listed campaign officials that reference a set of Russia-related keywords, marked Mr. Mueller’s first official order for information from the campaign, according to the person. The subpoena didn’t compel any officials to testify before Mr....