Born in Pune, Maharashtra, India Arjun started swimming at the age of 5 coached by his father G Muralidharan a former athlete, Ranji Trophy cricketer and Commander, Indian Navy.

Arjun, the younger brother of Amar Muralidharan, is a former police officer working at the Border Security Force since 2002 up until 2014 under the sports recruitment program.

[5] Based on his performances in the Senior Nationals Arjun was selected to represent India at the Commonwealth Youth Games which was held at Bendigo Australia in Dec 2004.

Arjun became the first and only Indian to win a medal coming third in the 200 meters Butterfly with a time of 2:06.99 beating teammate Rehan Poncha by .02 secs.

Became the best swimmer at the 53rd All India Police Aquatic Championships held at Talkatora Complex, New Delhi[8] In 2005 at the 1st Asian Indoor Games held from 13 to 17 November 2005 at the SAT Swimming Pool, Huamark Sports Complex in Bangkok, Thailand Arjun became the first Indian swimmer to win a silver medal in the 200 meters butterfly event clocking 2:03.33 behind Won Jae-Yun of Korea.

[12][13][14] Training in Quebec under the aegis of Sports Authority of India and the central government, Arjun along with elder brother Amar, participated under the banner of Laval University in the Speedo Eastern Canadian swimming championships held from 16–19 February in Montreal.

[25][26] Arjun trained at Toronto Swim club under former Munich Olympics 100 M Butterfly finalist Byron MacDonald and John Grootveld head coach at TSC.

[27] In 2008 Canada Cup Arjun won a bronze medal and broke the short course 200 butterfly national record clocking 1:59.45 and becoming the first Indian swimmer to break the 2 mins barrier in the event.

He returned to Toronto Canada and resumed swimming training late in July which affected his performances at the 2009 Open Nationals due to the long 6-month layoff and fracture rehabilitation process.

[32] Was adjudged the best swimmer for the 7th time in his career in the All India Police Aquatic Championships held at Thiruvananthapuram, Kerala with 5 gold medals and 2 meet records.

[36] He has endorsed sportswear company Metal Mulisha and is also sponsored by Siddhi Health Club located at Kothrud, Pune where he has done his strength training since 2002.