The Duchess was set to deliver the keynote address at the opening of an art installation commemorating children who died as a result of suffering harm on social media on Tuesday.
Meghan cancelled the plan, a spokesperson for the couple confirmed, but attended alongside her husband Prince Harry, who delivered a speech.
As they arrived, the pair made no comment while a large pack of journalists shouted to ask Meghan how she was feeling.
According to The Daily Telegraph, Meghan, who said in a statement last month she was "deeply distressed" at the allegations about her father, did not feel strong enough to speak at the gathering in Brussels.
US authorities charged Thomas Markle last week with possessing child sexual abuse photos, alleging photographs of himself with naked underage girls were found in rented storage units in California.
The 82-year-old denied the accusations when they came to light and entered no plea at an initial court appearance on Friday.
US Magistrate Judge Lindsay Griffin ordered a psychiatric evaluation, questioning whether he was competent to face prosecution.
The judge permitted Markle to be released from custody on the condition he submit to home detention and electronic monitoring.
Markle was most recently residing in Lakeland, Florida, where according to the Daily Mail newspaper, he was a nursing home patient.
Both Harry and Meghan have regularly spoken out about online dangers to children and been critical of major tech companies for not doing more to protect them.
The prince made no reference to his father-in-law in his address as the couple opened the Lost Screen Memorial, which they initially launched in New York last year through their charitable organisation Archewell.
"How did we reach a point where we can build technology capable of extraordinary things, yet still struggle to make it safe for a child?" Harry said, alongside parents who had been affected by the issue.
"I'm not here as an expert or a politician. I'm here as a father, my wife, as a mother and together, as a couple who stand alongside parents like Sandra, Megan and Sewell — in New York, Los Angeles, Geneva and now Brussels.
"Parents who never imagined they would have a reason to be in rooms like this," he said, referring to those who believe their children died as a result of online harm.
Meghan has been estranged from her father since the run-up to her marriage to King Charles' younger son in 2018.
She said in her statement last month she had known about the allegations against him since that year and had prevented him from having contact with her children Archie, 7, and Lilibet, 5, to protect them.
The couple's appearance in Nottingham in October was their first joint appearance since they moved back to live in Britain, having relocated to the United States in 2020 when they stepped back from official royal duties.
1800 RESPECT (1800 737 732)
National Sexual Abuse and Redress Support Service 1800 211 028
