Actually Muslims do have missionaries like Christianity but they are not called missionaries, rather they are called Tablighi Jamaat.
See details about their work and practices on wiki here:
About Tablighi Jamaat
First paragraph from this link, for lazy people like me.
Tablighi Jamaat (Urdu: تبلیغی جماعت, Tablīghī Jamā‘at; Arabic: جماعة التبليغ, Jamā‘at at-Tablīgh; Bengali: তাবলীগ জামাত; Hindi: तबलीग़ी जमात; English: Society for spreading faith) is a global Sunni Islamic proselytizing and revivalist movement that focuses on urging Muslims to return to orthodox Sunni Islam, and particularly in matters of ritual, dress, and personal behavior. The organisation is estimated to have between 12 million and 150 million adherents (the majority living in South Asia), and a presence in somewhere between 150 and 213 countries. It has been called "one of the most influential religious movements in 20th century Islam".
references are available on wikipedia
Before voting down you should actually change the question or read the definition of a missionary. It's almost same what Tablighi Jamaat. Also if you hate this Jamaat then I cannot help you sorry, secondly I have mentioned its name because it holds largest religious gathering each year more then Hajj Pilgrims in Pakistan, India and Bangladesh.
Here is the defination of Missionaries
plural noun: missionaries
a person sent on a religious mission, especially one sent to promote Christianity in a foreign country.