Muktar made his first international appearances in 2011, taking seventh place in the junior race at the 2011 IAAF World Cross Country Championships (sharing the team silver medal) and finishing fourth in the 10,000 metres at the 2011 African Junior Athletics Championships with a time of 28:44.95 minutes.
He began to raise his profile in 2012 with two prominent wins on the junior stage. First he defeated Kenyan opposition to win at the 2012 African Cross Country Championships, and then he went on to take the 5000 metres gold medal at the 2012 World Junior Championships in Athletics. He performed well in the 5000 m that year, taking the Ethiopian team (in the absence of many established runners). He won over the distance at the Meeting Lille Métropole and competed on the Diamond League for the first time, setting a best of 13:04.34 minutes at the Meeting Areva in Paris. He had podium finishes on the Italian road circuit towards the end of the year, coming third at the Giro di Castelbuono and close to victory at the BOClassic, where he recorded the same time as winner Imane Merga.
He performed well in cross country at the start of 2013, winning the Campaccio, Cross della Vallagarina and Cinque Mulini races. He followed this up with a bronze in the 2013 IAAF World Cross Country Championships in the junior race behind compatriot Hagos Gebrhiwet. In his first road outing of the year he won the Giro Media Blenio race.
In Stockholm, August 21st 2014 he recorded the fastest time in the world so far that year with 12:54.83.
- 3000 metres: 7:47.99 minutes (2014)
- 5000 metres: 12:54.83 minutes (2014)
- 10,000 metres: 28:54.95 minutes (2011)
- 10 km road: 28:11 minutes (2013)
- 2011 World Cross Country Junior Men's Race Results. IAAF. Retrieved on 2013-01-26.
- 2011 African Junior Championships. World Junior Athletics History. Retrieved on 2013-01-26.
- Williamson, Norrie (2012-03-19). Langat and Chepkirui take African XC titles in Cape Town. IAAF. Retrieved on 2012-03-25.
- Valiente, Emeterio (2012-07-14). Barcelona 2012 - Event Report - Men's 5000m Final. IAAF. Retrieved on 2013-01-26.
- Negash, Elshadai (2012-06-14). Driba and Endris impress at Ethiopian Champs. IAAF. Retrieved on 2013-01-26.
- Sampaolo, Diego (2012-09-27). T. Bekele impresses with 10km victory in Castelbuono - REPORT. IAAF. Retrieved on 2013-01-26.
- Sampaolo, Diego (01-02-2013). Favourites Merga and Kibet win in Bolzano. IAAF. Retrieved on 2013-01-26.
- Sampaolo, Diego (2013-01-06). Edris and Degefa take Ethiopian double at Campaccio. IAAF. Retrieved on 2013-02-18.
- Sampaolo, Diego (2013-02-03). Ethiopia's Edris and Godfay take the Cinque Mulini honours. IAAF. Retrieved on 2013-02-18.
- Sampaolo, Diego (2013-04-01). Edris adds his name to illustrious list of winners in Dongio . IAAF. Retrieved on 2013-04-02.