The man, who had not been identified, tried to get into the offices of radio and television broadcaster MBC in Riyadh Saturday to look for hostess Ghada al-Ali, Gulf News said local news website Sabq reported.
The man was angry that al-Ali had not responded to his Twitter messages, police said.
"After the program, they informed me that they detained a man armed with a gun who was looking for me to kill me," al-Ali told Sabq.
Police said they were investigating the incident.
"I heard that he told investigators that I had ignored him and that I had not replied to his messages on my Twitter account. I was able to go home normally, but my family has been shaken by this incident," al-Ali said.