The reason Jesus said this has been the subject of debate. One common belief is that He didn't want her to tarry there, that it was more of a "now is not the time" statemen. Example:
Clarke's Commentary on the Bible
Touch me not - Μη μου ἁπτου, Cling not to me. Ἁπτομαι has this sense
in Job 31:7, where the Septuagint use it for the Hebrew דבק dabak,
which signifies to cleave, cling, stick, or be glued to. From Matthew
28:9, it appears that some of the women held him by the feet and
worshipped him. This probably Mary did; and our Lord seems to have
spoken to her to this effect: "Spend no longer time with me now: I am
not going immediately to heaven - you will have several opportunities
of seeing me again: but go and tell my disciples, that I am, by and
by, to ascend to my Father and God, who is your Father and God also.
Therefore, let them take courage."
Another view:
Vincent's Word Studies
Touch me not (μή μοῦ ἅπτου)
The verb, primarily, means to fasten to. Hence it implies here, not a
mere momentary touch, but a clinging to. Mary thought that the old
relations between her Lord and herself were to be renewed; that the
old intercourse, by means of sight, sound, and touch, would go on as
before. Christ says, "the time for this kind of intercourse is over.
Henceforth your communion with me will be by faith through the Spirit.
This communion will become possible through my ascending to the
Father."
And another, similar to the others, but emphasizing "There are other things to do right now".
People's New Testament
20:17 Touch me not. She was probably about to clasp his feet. She is
told to discharge a higher duty: to go to the brethren with the glad
story.
