Did Jesus wear tsitsiyot? According to the NIV, Mathew 9:20-21:


  Just then a woman who had been subject to bleeding for twelve years
  came up behind him and touched the edge of his cloak. She said to
  herself, “If I only touch his cloak, I will be healed.”


Some websites, such as this and that, claim that the "edge of his cloak" refers to a tzitzit, or traditional Jewish fringes. Is this a reasonable inference based on this passage?
The answer to your question 'Did Jesus wear tsitsiyot?' is, yes he did. We can know this by looking at a few things:


Jesus (Yeshua) was a Jew born in first-century Israel (Matthew 1 &amp; 2):



  Matthew 1:1-17 (ESV) — 1 The book of the genealogy of Jesus Christ, the son of David, the son of Abraham ...
  
  Matthew 2:1 (ESV) — 2 Now after Jesus was born in Bethlehem of Judea in the days of Herod the king, behold, wise men from the east came to Jerusalem,



He came to fulfill the Law and the Prophets, and confirmed their authority:



  Matthew 5:17-18 (ESV) — 17 "Do not think that I have come to abolish the Law or the Prophets; I have not come to abolish them but to fulfill them. 18 For truly, I say to you, until heaven and earth pass away, not an iota, not a dot, will pass from the Law until all is accomplished.



He lived a life obedience to Yahweh's law – the Torah:



  John 15:10 (ESV) — If you keep my commandments, you will abide in my love, just as I have kept my Father's commandments and abide in his love.



In which, one of Yahweh's commands is for tzitzit be worn:



  Numbers 15:37-40 (ESV) — 37 The Lord said to Moses, 38 "Speak to the people of Israel, and tell them to make tassels on the corners of their garments throughout their generations, and to put a cord of blue on the tassel of each corner. 39 And it shall be a tassel for you to look at and remember all the commandments of the Lord, to do them, not to follow after your own heart and your own eyes, which you are inclined to whore after. 40 So you shall remember and do all my commandments, and be holy to your God.



Scripture defines sin as lawlessness (essentially Torah-lessness):



  1 John 3:4 (ESV) — 4 Everyone who makes a practice of sinning also practices lawlessness; sin is lawlessness.



Scripture frequently confirms after his death that he was without sin, meaning he did not break God's law:



  2 Corinthians 5:21 (ESV) — 21 For our sake he made him to be sin who knew no sin, so that in him we might become the righteousness of God.
  
  Hebrews 4:15 (ESV) — 15 For we do not have a high priest who is unable to sympathize with our weaknesses, but one who in every respect has been tempted as we are, yet without sin.
  
  1 Peter 2:22 (ESV) — 22 He committed no sin, neither was deceit found in his mouth.
  
  1 John 3:5 (ESV) — 5 You know that he appeared in order to take away sins, and in him there is no sin.


Lastly, just as in the example @disciple noted (Matt. 23:5) – the same Greek word used to identify the edge of Jesus's garment (in which the woman touched and was healed), is the exact same Greek word (kraspedon, g2899) used to identify the Pharisees tzitzit (tassels).

Because of this, we can safely answer your question that: Yes this is a reasonable inference based on this passage.