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,[5][6] and particularly in matters of ritual, dress, and personal behavior.[7] The organisation is estimated to have between 12 million[8] and 150 million adherents[3] (the majority living in South Asia[9]), and a presence in somewhere between 150[8] and 213 countries.[3] It has been called "one of the most influential religious movements in 20th century Islam".[10]
references are available on wikipedia
[UPDATE]
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
mis·sion·ar·y
ˈmiSHəˌnerē/
noun
plural noun: missionaries
a person sent on a religious mission, especially one sent to promote Christianity in a foreign country.