This past week a lady told my wife that it is forbidden to wash a Shaitel - Wig during the three weeks. To the best of my knowledge I have never seen such a prohibition. Is there a source that prohibits washing a wig during the three weeks?
I could not find a single instance of a Posek forbidding washing or laundering anything during the (first 2 weeks of the) 3 weeks.
I searched the Shulchan Aruch, Kitzur SA, Kitzur Yalkut Yosef and Aruch HaShulchan
Even during the 9 days (or the week during which Tish'a B'Av falls, as per the Sefardim) when most laundering is forbidden, clothes that get soiled often and one has a finite supply - like cloth diapers - may be washed.
Similarly, anything a woman needs for her 7-clean days may be laundered, as a Mitzvah trumps the custom of not washing.
I would venture to say that if a woman is in the habit of washing her wig every few days because it gets very sweaty, for example, then she may be allowed to do so even during the 9 days since she can't be expected to have a wig collection.
וְאִשָּׁה שֶׁצְּרִיכָה לִלְבּוֹשׁ לְבָנִים לִסְפֹּר ז' נְקִיִּים, מֻתֶּרֶת לְכַבֵּס וְלִלְבּוֹשׁ
וְכֵן הַמִּטְפָּחוֹת שֶׁמְלַפְּפִין בָּהֶן אֶת הַתִּינוֹקוֹת [חִתּוּלִים], שֶׁמְלַכְלְכִין אוֹתָן תָּדִיר, מֻתָּר לְכַבְּסָ
- Kitzur Shulchan Aruch 122:9