The 'Zero Defect, Zero Effect' initiative is aimed at promoting high quality in manufacturing processes while ensuring that environmental impacts are minimized. Let's analyze each given option:

1. Ministry of Heavy Industries: Primarily concerned with the development of the heavy industry sector, their initiatives focus on expanding industrial capacities rather than directly promoting sustainable practices at the micro level.
2. Ministry of Education: Focused on educational reforms, capacity building, and curriculum development. This initiative does not align with the Ministry's primary functions.
3. Ministry of Skill Development and Entrepreneurship: While related to skill development that could indirectly support quality enhancement, the initiative does not directly relate to skill development at the individual level.
4. Ministry of Micro, Small and Medium Enterprises: This Ministry oversees initiatives that bolster the MSME sector, which includes enhancing manufacturing quality and environmental sustainability at the grassroots level. The 'Zero Defect, Zero Effect' initiative is developed to help MSMEs produce world-class products with minimal environmental impact.

Therefore, the correct answer is Ministry of Micro, Small and Medium Enterprises. This initiative under the Ministry is strategically significant for boosting India's manufacturing capabilities while keeping environmental considerations in check, aligning with the broader objectives of sustainable development.