FRANKFURT—A Chinese takeover bid for Aixtron SE of Germany collapsed Thursday, a week after U.S. President Barack Obama blocked the deal on national-security grounds, according to a statement from the buyer.

The €670 million ($721 million) offer for the semiconductor company was thrown into question this fall when Germany’s economic ministry raised security concerns about the bid, made by Fujian Grand Chip Investment Fund LP’s German unit. These concerns were echoed by authorities in the U.S., resulting in last week’s outright...