Special Counsel Robert Mueller has impaneled a grand jury in Washington to investigate Russia’s interference in the 2016 elections, a sign that his inquiry is growing in intensity and entering a new phase, according to people familiar with the matter.

The grand jury, which began its work in recent weeks, signals that Mr. Mueller’s inquiry will likely continue for months. Mr. Mueller is investigating Russia’s efforts to influence the 2016 election and whether President Donald Trump’s campaign or associates colluded with the...