Rayouf al-Humedhi emailed her suggestion to the Unicode Consortium, a non-profit corporation that reviews and develops new emojis.
She received a reply from a member of a Unicode subcommittee, offering to help her draft a formal proposal.
"We applaud Unicode for the diversification of emojis in recent years," she wrote in her seven-page proposal draft.
"However, this does not mean it should stop now. With the amount of difference in this world, we must be represented."
A graphic designer supporting the idea contributed with a proposed design for the emoji.
Her idea has won the support of Reddit co-founder Alexis Ohanian, as well as social media users from various countries.
According to the 15-year-old high school student, the idea began when her friends wanted to identify themselves to one another in a WhatsApp group chat, using unique emojis instead of their names.
Humedhi, who wears the hijab, could not find an emoji to represent her.
"I wanted something to represent me, alongside the millions of women who wear the headscarf every day, and pride themselves on wearing the headscarf," she said in a Skype interview, according to The Washington Post.
Humedi argued that the emoji would not only represent Muslim women, but also Orthodox Jews and Christians who wear some form of the headscarf.
She hopes adding an emoji wearing the headscarf would "promote diversity and tolerance".
The proposal is aiming for formal consideration in November. If approved, the new emoji could be announced as early as mid-2017.
Humedhi's proposal comes as the debate about the different forms of the Muslim veil is ongoing in different countries across the world, especially in Europe.The issue raises questions of religious freedom, women's rights and islamophobia.