Julieth Gonzales Theran was reporting from Saransk when a bearded man came from the right of the shot, grabbed her and kissed her on the cheek.
The journalist, who did not pause her piece to camera during or after the incident, was working for the Spanish news channel of German network Deutsche Welle.
Ms Theran says she has been working in sports reporting for a long time and she has never been attacked, even though she was "exposed to the fans and some crazy people".
She adds that she is now unable to do her job without additional security.
After receiving messages of support on social media, she said: "I am overwhelmed and grateful for all the voices and solidarity expressed after this incident.
"I don't want to be a victim, I want to do the job I love.
"Unfortunately, the incident has meant that I cannot report from Russia as I had planned, only in a limited form and with more security. But enough of that!
"Today the man who assaulted me may be the subject, but from tomorrow I would like to be able to talk about football again.
"To experience this World Cup and to work here was and is my dream. I won't let him take away from me."
Her employer said the attack amounted to "sexual violence" and should not be tolerated.
DW editor-in-chief Ines Pohl said: "Here, too, the zero tolerance rule applies and any harassment like this is unacceptable.
"We must all work to ensure that female reporters can also do their job at major sporting events.
"And that starts with calling a spade a spade: this is not a trivial offence, but sexual violence."
