The exercise was part of two days of training she attended with Prince Harry in Herefordshire, whom she is due to marry in May.
This occasion marks the first official event involving both Markle and Queen Elizabeth.
Meghan and Harry are set to tie the knot in St George's Chapel in Winsdor Castle in May, and it was previously reported that the brunette beauty has been turning to Harry's step-mother Duchess Camilla for support.
Instead, Prince William could be set to fill in and walk her down the aisle - despite Markle reportedly preferring for her mum to give her away.
It will be just as important to Will and Harry's father, Prince Charles the Prince of Wales, when he succeeds her as monarch and as head of the Commonwealth: he has already taken over significant aspects of her role since the 91-year-old queen began cutting back on worldwide travel some years ago.
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Elizabeth has been head of the Commonwealth since 1952 and aides say she regards the success of the organisation, which now has 53 members representing over 2.4 billion people, as one of her greatest achievements as queen.
Markle was wearing a long white coat fastened only at the waist with a small round beret-style hat in white perched on the side of her head.
In her Commonwealth Day message, which will feature in the service, the Queen has praised the "Commonwealth connection" that allows people from different nations to bond and celebrate "diversity".
The queen wore a wine-colored coat and matching hat, along with a large diamond brooch.
They were joined by Harry's brother, Prince WIlliam, the Duke of Cambridge, and Catherine, Duchess of Cambridge, and Markle's future father in-law, Prince Charles. After the service, the Queen and other royals met those involved in the ceremony.