Mahmoud Houda decided to take up football after watching his older brother, Hassan Rasmy, who became one of the founders of the Al Ittihad Alexandria Club. Houda demonstrated considerable skill at a young age and soon found numerous local Alexandria clubs racing to recruit him. He eventually settled in with Ittihad and, during his tenure, won the Egypt Cup twice (1926 and 1936) and the Sultan Hussein Cup once (1935). He was also a long-time member of the Egyptian national squad and was selected to represent his country in its début at the 1920 Antwerp Olympics. While he did not actually make the trip that year, he did take part in the 1924 and 1928 tournaments, where Egypt was eliminated in the quarterfinals and the bronze medal match respectively. He retired in 1937 due to injuries, but soon transitioned into coaching and management with his former club. His younger brother, Sayed, was also a footballer with Ittihad and took part in the 1924 and 1928 Olympic Games as well.