"Family is family," said Ms Grant, taking exception to Ms Markle ignoring her and her family for her wedding, reported Fox News, according to news agency ANI.
In a tweet, Ms Grant said that the matter of being close to family is not "at issue", adding, "Humanitarians move forward with love and kindness especially to Family".
"I have an uncle I have only seen once but I would never say he is not family because we are not close. Humanitarians move forward with love and kindness especially to Family," she added.
In another tweet, Ms Grant also claimed that she and Ms Markle are both 15th cousins with Prince Harry. To show proof, Ms Grant posted a Markle family tree, which allegedly proves that the estranged sisters are related to Prince Harry.
"And it's not only Meg who is 15th cousin to Harry. My brother and I are also. I was the first born Markle to my father. Exclude the [Markles] from this wedding would be highly inappropriate," Ms Grant said in a tweet.
Ms Markle is meanwhile, busy with wedding preparations, which are said to have stringent security measures, with barriers to stop vehicle attacks, armed patrols and airport-style security.
Prince Harry and Meghan Markle are set to tie the knot at St George's Chapel in Windsor Castle on May 19, which is Queen Elizabeth's residence at the city of Windsor.
Another guest is Amelia Thompson, a 12-year-old, who attended pop star Ariane Grande's concert last year, which was subject to an attack in which 22 people, including seven children were killed and 500 were injured.
The wedding will also involve the royal couple donating to seven different charities, among which is the Myna Mahila Foundation, a Mumbai-based non-profit, which manufactures and sells affordable sanitary pads.
(With Inputs From ANI)