This is basically stated by the Pele Yoets (entry: Zohar) who writes:
למוד ספר הזוהר נשגב מאד לטהר ולקדש הנפש ואפילו אי לא ידע מאי קאמר...ראוי לכל אדם ליקח לו ספר הזוה"ק ולא יעבור מלקרוא הפרשה מדי שבוע בשבוע וזה גדר גדול לאדם כדי שלא ישיאנו יצרו לפנות עצמו לבטלה שהוא רעה גדולה כידוע ויעשה זאת אפוא וינצלו
The study of the Zohar is very auspicious to purify and sanctify the soul and even if one doesn't know what he is saying...it is appropriate for every person to get for himself the Zohar and not fail to read the weekly parasha each week, and this is great restraint for a person that his inclination not succeed in drawing him to frivolity, which is a great sin as is known, and he should do this and be victorious.
An earlier source for this is R. Nattan Shapira (17th cent.) who writes in the end of Tuv Haarets (cited here) that one should read the Zohar even without understanding and that this has a great effect on the soul:
צריך לקרות בספר הזוהר וכו' אף על גב דלא ידע מאי קאמר, כי תיקון גדול ועצם מאוד למטרוניתא ולנשמתו כנודע מכמה טעמים
Similarly, the Hida in Shem Hag'dolim (Ma'arekhet Sefarim: Bahir) writes that he was asked about the funny anomaly the students of the Arizal teach that there is great significance to learning the Zohar without understanding, but apparently there isn't great significance learning other works without understanding, like the Mishna, or Tanakh. He explains that indeed this is the case, since the Zohar explicitly teaches the secrets of the Torah so reading it affects the soul.