"Unfortunately, my family and I closed out 2020 learning that we had contracted COVID while in California over the holidays," Morgan wrote on social media. "We are all in good spirits and recovering well.
"After our isolation is completed, I will follow U.S. Soccer's return to play guidelines to ensure my body is fully recovered and I can join my teammates back on the field soon. Be safe and Happy New Year."
The U.S. women's team will reveal the roster for its annual January training camp Wednesday.
The 31-year-old Morgan spent the first half of the 2020-21 season with Tottenham Hotspur before announcing last month she was returning to the National Women's Soccer League's Orlando Pride this year.
Morgan has amassed 170 caps at the international level and helped guide the USWNT to the gold medal at the 2012 Olympics. Morgan and the U.S. women's squad also have won the last two FIFA World Cup titles, including their 2019 victory in France.