Pichai said: "We're concerned about the impact of this order and any proposals that could impose restrictions on Googlers and their families, or that could create barriers to bringing great talent to the US."
Several major technology companies have criticised the travel ban.
Tim Cook, CEO of Apple said: "Apple would not exist without immigration, let alone thrive and innovate the way we do."
Apple's founder Steve Jobs was the son of a Syrian immigrant.
Netflix CEO Reed Hastings called the president's first week in office "very sad", saying in a Facebook post that 'Trump's actions are hurting Netflix employees around the world, and are so un-American it pains us all.
"It is time to link arms together to protect American values of freedom and opportunity."
Trump's hardline executive order, signed Friday, suspends the arrival of refugees for at least 120 days, and for the next three months bars visas for travelers from seven Muslim-majority countries: Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen.
As resistance to the temporary immigration restrictions mount, a US federal judge on Saturday ordered authorities to stop deporting refugees and other travelers stuck at US airports.
US District Judge Ann Donnelly's decision to issue a temporary stay - which stopped short of ruling on the constitutionality of Trump's order - came after dozens of people were detained at US airports following Trump's actions.
Microsoft's CEO Satya Nadella said: "As an immigrant and as a CEO, I've both experienced and seen the positive impact that immigration has on our company, for the country, for the world."
The company had warned Thursday that immigration restrictions could impact its ability to fill research and development positions.
Globalisation has been a boon for Silicon Valley, which employs a significant population of foreign engineers. Some 250,000 Muslims live in the San Francisco Bay Area, according to the Council on American-Islamic Relations.
"Internet companies in particular thrive in the US because the best and the brightest are able to create innovative products and services right here in America," said Michael Beckerman, the head of a leading industry lobby group.
Trump met last month with a handful of America's most powerful tech executives - a bid to mend fences with a largely pro-Democrat industry.
In the short term, many tech companies are offering legal assistance to staffers impacted by the executive order.
A Facebook spokesperson said: "We are assessing the impact on our workforce and determining how best to protect our people and their families from any adverse effects."
Chris Sacca, a major financial backer of the sector, vowed to donate $150,000 to the American Civil Liberties Union, an organization that has hit the executive order with legal challenges.
Uber CEO Travis Kalanick vowed to raise the issue at a meeting next week of Trump's business advisory council.
