Security chiefs intervened after Markle and Prince Harry were targeted by far-right threats.
A source told the Sun: "Nothing is more important to these guys than protecting the royal family. Meghan and Harry like to meet the public as much as possible and make contact with the crowds that come to see them.
"And although having a car door closed might seem like a trivial thing, it could be the difference. God forbid if anything did go wrong arriving at a royal engagement, but security need to be able to get them back into cars in seconds if needs be. If they're closed and locked, it's impossible."
This news comes just weeks after Markle's bodyguard quit, and less than a month after a neo-Nazi group branded Prince Harry a "race traitor" over the marriage.
Last February, Scotland Yard had to be called in after a letter was sent to Markle at Kensington Palace which contained a racist remark and a substance claimed to be deadly anthrax - it was later found to be harmless.