Cruz's call to stop NFL fans from buying protesting players' jerseys comes after multiple athletes joined San Francisco 49ers quarterback Colin Kaepernick in kneeling, sitting or raising a fist during The Star-Spangled Banner in a protest against racial bias and police brutality.
Several Miami Dolphins players took a knee on the sideline beside their teammates as the national anthem played before their season opener against the Seattle Seahawks on Sunday.
The Seattle Seahawks chose to stand with interlocked arms, rather than raising their hands to their hearts in a planned "demonstration of unity" to promote "justice for all people".
"I would like to keep moving forward in the right direction with everybody. Equal rights, equal opportunity," said Miami's Jelani Jenkins, one of the Dolphins to kneel. "From my position, it doesn't seem that it's happening. That's why I took a stand."
Also on Sunday, Kansas City Chiefs cornerback Marcus Peters raised his fist in the air during the anthem before his team's game against the San Diego Chargers.
Sunday also marked the 15th anniversary of the September 11 terrorist attacks and the players' peaceful protest on this day has divided many of Americans.
Cruz also retweeted model Kate Upton's tweet saying the decision not to stand was "unacceptable" and that the players should be "proud to be an American. Especially on 9/11."
Since the NFL season started earlier this month, dozens of players have joined Kaepernick in one form of protest or another, including women's soccer star Megan Rapinoe and several college players.
The NFL star's statement has sparked a national debate among athletes and fans alike.