Maathai, who won the Nobel in 2004 for her work in conservation and women's rights, resisted a government plan to build a complex at Uhuru Park, where the funeral was taking place.
"Wangari's legacy goes beyond Kenya -- all over the world," Odinga said. "We have lost a dedicated selfless Kenyan patriot," and her work will continue to inspire the rest of the world.
Maathai was seen as a threat to the rich and powerful. She was beaten, arrested and vilified for the simple act of planting a tree, a natural wonder she believed could reduce poverty and conflict.
Best known as the Tree Mother of Africa, Maathai believed that a healthy environment helped improve lives by providing clean water and firewood for cooking, thereby decreasing conflict. The Kenyan organization she founded planted 30 million trees, a triumph for nature that inspired the UN to launch a worldwide campaign that resulted in 11 billion trees planted.
Maathai died late last month after a long battle with cancer. She was 71.
On Friday, three other champions of women's rights in Africa and the Middle East were also awarded the peace prize.
The 2011 prize was split among Tawakkul Karman, a leader of anti-government protests in Yemen; Liberian President Ellen Johnson Sirleaf, and Leymah Gbowee, who campaigned against rape as a weapon in Liberia's brutal civil war.